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Номер 655, страница 202 - гдз по алгебре 8 класс учебник Дорофеев, Суворова
Авторы: Дорофеев Г. В., Суворова С. Б., Бунимович Е. А., Кузнецова Л. В., Минаева С. С., Рослова Л. О.
Тип: Учебник
Издательство: Просвещение
Год издания: 2019 - 2022
Цвет обложки: белый, бирюзовый, оранжевый
Допущено Министерством просвещения Российской Федерации
Популярные ГДЗ в 8 классе
Глава 4. Системы уравнений. 4.5. Решение систем уравнений способом подстановки. Упражнения - номер 655, страница 202.
App\Models\Task {#1030 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 209835 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "202" "field_page_end" => null "field_url" => "/8-klass/algebra/dorofeev-uchebnik/655" "field_display_title" => "655" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ 0 => App\Models\Branch {#1045 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 208946 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Системы уравнений" "field_branch_order" => "4" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ 0 => App\Models\Term {#1047 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "168" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1087 #items: array:1 [ 0 => App\Models\Book {#1049 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 80 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1051 #items: array:1 [ 0 => App\Models\Term {#1048 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6471 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алгебра" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "algebra" ] #original: array:10 [ "id" => 6471 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алгебра" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "algebra" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1052 #items: array:1 [ 0 => App\Models\Term {#1053 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ …6] "field_translit" => "vosmoj" ] #original: array:6 [ "id" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ …6] "field_translit" => "vosmoj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054 #items: array:1 [ 0 => App\Models\Term {#1055 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #original: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1056 #items: array:6 [ 0 => App\Models\Term {#1057 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4283 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Дорофеев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Георгий" "field_patronymic" => "Владимирович" "field_surname_rp" => null ] #original: array:12 [ "id" => 4283 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Дорофеев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Георгий" "field_patronymic" => "Владимирович" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1058 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5879 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Суворова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Светлана" "field_patronymic" => "Борисовна" "field_surname_rp" => null ] #original: array:12 [ "id" => 5879 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Суворова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Светлана" "field_patronymic" => "Борисовна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1059 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 3941 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Бунимович" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Евгений" "field_patronymic" => "Абрамович" "field_surname_rp" => null ] #original: array:12 [ "id" => 3941 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Бунимович" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Евгений" "field_patronymic" => "Абрамович" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Term {#1060 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4848 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кузнецова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Людмила" "field_patronymic" => "Викторовна" "field_surname_rp" => null ] #original: array:12 [ "id" => 4848 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кузнецова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Людмила" "field_patronymic" => "Викторовна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 4 => App\Models\Term {#1061 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5198 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Минаева" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Светлана" "field_patronymic" => "Станиславовна" "field_surname_rp" => null ] #original: array:12 [ "id" => 5198 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Минаева" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Светлана" "field_patronymic" => "Станиславовна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 5 => App\Models\Term {#1062 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1063 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1064 #items: array:1 [ 0 => App\Models\Term {#1065 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1066 #items: array:1 [ 0 => App\Models\Term {#1067 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1068 #items: array:1 [ 0 => App\Models\Term {#1069 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1070 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1071 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1072 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1073 #items: array:1 [ 0 => App\Models\Term {#1074 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_publication_number" => "7" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1075 #items: array:1 [ 0 => App\Models\Term {#1076 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1077 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => "2022" "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для общеобразовательных организаций" "field_allowed" => "Допущено Министерством просвещения Российской Федерации" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1206" "field_priority" => "14" "field_default_folder" => "/algebra_08/dorofeev/" "field_isbn" => null "field_cover" => array:1 [ 0 => "/media/algebra_08/dorofeev/covers/cover1.webp?ts=1734213765" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_08/dorofeev/covers/cover1.webp?ts=1734213765" "alt" => "" "width" => "1919" "height" => "2577" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1078 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1079 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1080 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/algebra/dorofeev-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1081 #items: array:3 [ 0 => App\Models\Term {#1082 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Term {#1083 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: 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пригодится. Так, по крайней мере думают подростки. Однако на практике все получается совершенно по-другому. Поэтому как бы сложен не был предмет (например, алгебра), его необходимо как следует изучить. Чтобы процесс восприятия материала проходил легко и без заминок, следует использовать «<strong>ГДЗ по Алгебре 8 класс Учебник Дорофеев, Суворова, Бунимович, Кузнецова, Минаева, Рослова (Просвещение)</strong>». </p> <p> В справочнике нашли отражение следующие темы: <ol> <li>Алгебраическая дробь, ее свойства, действия с ней.</li> <li>Как преобразовать степень?</li> <li>Теорема Пифагора.</li> <li>График зависимости y=√х.</li> <li>Квадратный и кубический корни.</li> <li>Двойные радикалы, и т.д.</li> </ol> <p> В восьмом классе по предмету проходят спаренные уроки, что с одной стороны должно помочь учителю более подробно объяснить каждую тему. Но на деле и этого времени все равно не хватает, так как программа стала еще обширнее. 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Так как самостоятельно подростки такого мониторинга не проводят, то им поможет в этом <strong>сборник ответов по алгебре 8 класс к учебнику Дорофеева</strong>. </p> <p> Благодаря изданию учащиеся смогут: <ol> <li>улучшить качество письменных работ;</li> <li>избавиться от любых недочетов;</li> <li>приобрести хорошую успеваемость;</li> <li>устранять трудности по мере их возникновения.</li> </ol> <p> Систематически занимаясь с решебником, восьмиклассники научатся не только разбираться в самых непростых темах, но и будут активно применять свои навыки на практике. Это позволит им выбиться в отличники и успешно справляться со всеми поставленными учителем задачами. Кроме того, они могут не переживать о результатах многочисленных проверочных работ, так как будут знать весь материал «на зубок». </p> <h2> Как часто можно использовать онлайн-справочник? </h2> <p> В скором времени учащимся предстоит сдавать первые экзамены, после чего многие из них навсегда покинут школьные стены. 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Освоив это, восьмиклассники не будут испытывать затруднений при переходе к более сложному материалу. </p>" "breadcrumbs" => array:3 [ "class" => 379 "subject" => 542 "class_subject" => 385 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1085 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 208946 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Системы уравнений" "field_branch_order" => "4" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050} "field_page_start" => "168" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1087} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1085} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1122 #items: array:3 [ 0 => App\Models\Branch {#1132 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 208946 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Системы уравнений" "field_branch_order" => "4" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1133 #items: array:1 [ 0 => App\Models\Term {#1047} ] #escapeWhenCastingToString: false } "field_page_start" => "168" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1134 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1135 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 208946 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Системы уравнений" "field_branch_order" => "4" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1133} "field_page_start" => "168" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1134} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1135} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Branch {#1136 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 208959 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "4.5. 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Решение систем уравнений способом подстановки" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1137} "field_page_start" => "198" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1138} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1139} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Branch {#1140 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 208961 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Упражнения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1141 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "201" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1142 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1151 #items: array:1 [ 0 => App\Models\Branch {#1150 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 208959 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "4.5. Решение систем уравнений способом подстановки" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1152 …2} "field_page_start" => "198" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1153 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1154 …2} ] #original: array:24 [ "id" => 208959 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "4.5. Решение систем уравнений способом подстановки" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1152 …2} "field_page_start" => "198" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1153 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1154 …2} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 208961 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Упражнения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1141} "field_page_start" => "201" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1142} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1151} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1120 #items: array:5 [ 0 => App\Models\Element {#1110 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 233566 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1101 #items: array:1 [ 0 => App\Models\Edition {#1111 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 729 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1109 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "tolik" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1107 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1106 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1105 …2} "field_content_source" => null ] #original: array:21 [ "id" => 729 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1109 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "tolik" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1107 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1106 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1105 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "209835" "type" => "task" ] "text" => "<p><strong>655</strong> Решите систему уравнений:</p><p><strong>а)</strong> $\begin{cases} x+y=12 \\ xy=32 \end{cases}$</p><p><strong>б)</strong> $\begin{cases} x-y=4 \\ xy=12 \end{cases}$</p><p><strong>в)</strong> $\begin{cases} y=x+2 \\ 4y+x^2=8 \end{cases}$</p><p><strong>г)</strong> $\begin{cases} y^2+2x-4y=0 \\ 2y-x=2 \end{cases}$</p><p><strong>д)</strong> $\begin{cases} 2x-y^2=5 \\ x+y^2=16 \end{cases}$</p><p><strong>е)</strong> $\begin{cases} x^2-3y=-5 \\ x^2-y=1 \end{cases}$</p>" "img" => array:1 [ 0 => array:5 [ "name" => "655-1.jpg" "alt" => null "width" => "1591" "height" => 403 "path" => "/media/algebra_08/dorofeev/0-00/655-1.webp?ts=1734264558" ] ] ] #original: array:7 [ "id" => 233566 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1101} "task" => array:2 [ "refs" => "209835" "type" => "task" ] "text" => "<p><strong>655</strong> Решите систему уравнений:</p><p><strong>а)</strong> $\begin{cases} x+y=12 \\ xy=32 \end{cases}$</p><p><strong>б)</strong> $\begin{cases} x-y=4 \\ xy=12 \end{cases}$</p><p><strong>в)</strong> $\begin{cases} y=x+2 \\ 4y+x^2=8 \end{cases}$</p><p><strong>г)</strong> $\begin{cases} y^2+2x-4y=0 \\ 2y-x=2 \end{cases}$</p><p><strong>д)</strong> $\begin{cases} 2x-y^2=5 \\ x+y^2=16 \end{cases}$</p><p><strong>е)</strong> $\begin{cases} x^2-3y=-5 \\ x^2-y=1 \end{cases}$</p>" "img" => array:1 [ 0 => array:5 [ "name" => "655-1.jpg" "alt" => null "width" => "1591" "height" => 403 "path" => "/media/algebra_08/dorofeev/0-00/655-1.webp?ts=1734264558" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1086 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 237058 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1126 #items: array:1 [ 0 => App\Models\Edition {#1088 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 730 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 1" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1034 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1039 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1121 …2} "field_content_source" => null ] #original: array:21 [ "id" => 730 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 1" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1034 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1039 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1121 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "209835" "type" => "task" ] "img" => array:6 [ 0 => array:5 [ "name" => "655-1.png" "alt" => null "width" => "705" "height" => 1985 "path" => "/media/algebra_08/dorofeev/1-00/655-1.webp?ts=1734266183" ] 1 => array:5 [ "name" => "655-2.png" "alt" => null "width" => "705" "height" => 1985 "path" => "/media/algebra_08/dorofeev/1-00/655-2.webp?ts=1734266183" ] 2 => array:5 [ "name" => "655-3.png" "alt" => null "width" => "705" "height" => 1843 "path" => "/media/algebra_08/dorofeev/1-00/655-3.webp?ts=1734266183" ] 3 => array:5 [ "name" => "655-4.png" "alt" => null "width" => "705" "height" => 2088 "path" => "/media/algebra_08/dorofeev/1-00/655-4.webp?ts=1734266183" ] 4 => array:5 [ "name" => "655-5.png" "alt" => null "width" => "705" "height" => 2022 "path" => "/media/algebra_08/dorofeev/1-00/655-5.webp?ts=1734266183" ] 5 => array:5 [ "name" => "655-6.png" "alt" => null "width" => "705" "height" => 2155 "path" => "/media/algebra_08/dorofeev/1-00/655-6.webp?ts=1734266183" ] ] ] #original: array:6 [ "id" => 237058 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1126} "task" => array:2 [ "refs" => "209835" "type" => "task" ] "img" => array:6 [ 0 => array:5 [ "name" => "655-1.png" "alt" => null "width" => "705" "height" => 1985 "path" => "/media/algebra_08/dorofeev/1-00/655-1.webp?ts=1734266183" ] 1 => array:5 [ "name" => "655-2.png" "alt" => null "width" => "705" "height" => 1985 "path" => "/media/algebra_08/dorofeev/1-00/655-2.webp?ts=1734266183" ] 2 => array:5 [ "name" => "655-3.png" "alt" => null "width" => "705" "height" => 1843 "path" => "/media/algebra_08/dorofeev/1-00/655-3.webp?ts=1734266183" ] 3 => array:5 [ "name" => "655-4.png" "alt" => null "width" => "705" "height" => 2088 "path" => "/media/algebra_08/dorofeev/1-00/655-4.webp?ts=1734266183" ] 4 => array:5 [ "name" => "655-5.png" "alt" => null "width" => "705" "height" => 2022 "path" => "/media/algebra_08/dorofeev/1-00/655-5.webp?ts=1734266183" ] 5 => array:5 [ "name" => "655-6.png" "alt" => null "width" => "705" "height" => 2155 "path" => "/media/algebra_08/dorofeev/1-00/655-6.webp?ts=1734266183" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Element {#1103 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 235684 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1095 #items: array:1 [ 0 => App\Models\Edition {#1104 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 731 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1098 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_content_source" => null ] #original: array:21 [ "id" => 731 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_content_type" => "free" "field_content_mode" => "image" 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"width" => "511" "height" => 1201 "path" => "/media/algebra_08/dorofeev/2-00/655-1.webp?ts=1734264843" ] ] ] #original: array:6 [ "id" => 235684 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1095} "task" => array:2 [ "refs" => "209835" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "655-1.png" "alt" => null "width" => "511" "height" => 1201 "path" => "/media/algebra_08/dorofeev/2-00/655-1.webp?ts=1734264843" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Element {#1097 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 235856 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:1 [ 0 => App\Models\Edition {#1096 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 732 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 3" "field_order" => "4" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "3-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1089 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1090 …2} "field_content_source" => null ] #original: array:21 [ "id" => 732 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 3" "field_order" => "4" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "3-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1089 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1090 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "209835" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "655-1.jpg" "alt" => null "width" => "338" "height" => 2299 "path" => "/media/algebra_08/dorofeev/3-00/655-1.webp?ts=1734264902" ] ] ] #original: array:6 [ "id" => 235856 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1043} "task" => array:2 [ "refs" => "209835" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "655-1.jpg" "alt" => null "width" => "338" "height" => 2299 "path" => "/media/algebra_08/dorofeev/3-00/655-1.webp?ts=1734264902" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 4 => App\Models\Element {#1128 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1373823 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1148 #items: array:1 [ 0 => App\Models\Edition {#1130 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 4" "field_order" => "5" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1127 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "vadim" "field_edition_type" => "solution" "field_root_dir" => "4-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1144 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1143 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 4" "field_order" => "5" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1127 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "vadim" "field_edition_type" => "solution" "field_root_dir" => "4-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1144 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1143 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "209835" "type" => "task" ] "text" => "<p><strong>а)</strong> $ \begin{cases} x + y = 12, \\ xy = 32. \end{cases} $</p><p>Это система, которую удобно решить с помощью теоремы Виета для квадратного уравнения. Числа $x$ и $y$ являются корнями квадратного уравнения $t^2 - (x+y)t + xy = 0$.</p><p>Подставим значения из системы:</p><p>$t^2 - 12t + 32 = 0$</p><p>Решим это квадратное уравнение. Дискриминант $D = b^2 - 4ac = (-12)^2 - 4 \cdot 1 \cdot 32 = 144 - 128 = 16$.</p><p>Корни уравнения:</p><p>$t_1 = \frac{-b + \sqrt{D}}{2a} = \frac{12 + \sqrt{16}}{2} = \frac{12 + 4}{2} = \frac{16}{2} = 8$</p><p>$t_2 = \frac{-b - \sqrt{D}}{2a} = \frac{12 - \sqrt{16}}{2} = \frac{12 - 4}{2} = \frac{8}{2} = 4$</p><p>Таким образом, пары решений $(x, y)$ — это $(8, 4)$ и $(4, 8)$.</p><p>Ответ: $(4, 8)$, $(8, 4)$.</p><p><strong>б)</strong> $ \begin{cases} x - y = 4, \\ xy = 12. \end{cases} $</p><p>Воспользуемся методом подстановки. Выразим $x$ из первого уравнения:</p><p>$x = 4 + y$</p><p>Подставим это выражение во второе уравнение:</p><p>$(4 + y)y = 12$</p><p>$4y + y^2 = 12$</p><p>$y^2 + 4y - 12 = 0$</p><p>Решим полученное квадратное уравнение. По теореме Виета, корни $y_1 = -6$ и $y_2 = 2$.</p><p>Найдем соответствующие значения $x$:</p><p>Если $y_1 = -6$, то $x_1 = 4 + (-6) = -2$.</p><p>Если $y_2 = 2$, то $x_2 = 4 + 2 = 6$.</p><p>Получаем две пары решений.</p><p>Ответ: $(-2, -6)$, $(6, 2)$.</p><p><strong>в)</strong> $ \begin{cases} y = x + 2, \\ 4y + x^2 = 8. \end{cases} $</p><p>Используем метод подстановки. Подставим выражение для $y$ из первого уравнения во второе:</p><p>$4(x + 2) + x^2 = 8$</p><p>$4x + 8 + x^2 = 8$</p><p>$x^2 + 4x = 0$</p><p>Вынесем $x$ за скобки:</p><p>$x(x + 4) = 0$</p><p>Отсюда $x_1 = 0$ или $x_2 = -4$.</p><p>Найдем соответствующие значения $y$:</p><p>Если $x_1 = 0$, то $y_1 = 0 + 2 = 2$.</p><p>Если $x_2 = -4$, то $y_2 = -4 + 2 = -2$.</p><p>Получаем две пары решений.</p><p>Ответ: $(0, 2)$, $(-4, -2)$.</p><p><strong>г)</strong> $ \begin{cases} y^2 + 2x - 4y = 0, \\ 2y - x = 2. \end{cases} $</p><p>Применим метод подстановки. Выразим $x$ из второго уравнения:</p><p>$x = 2y - 2$</p><p>Подставим это выражение в первое уравнение:</p><p>$y^2 + 2(2y - 2) - 4y = 0$</p><p>$y^2 + 4y - 4 - 4y = 0$</p><p>$y^2 - 4 = 0$</p><p>$(y - 2)(y + 2) = 0$</p><p>Отсюда $y_1 = 2$ или $y_2 = -2$.</p><p>Найдем соответствующие значения $x$:</p><p>Если $y_1 = 2$, то $x_1 = 2(2) - 2 = 4 - 2 = 2$.</p><p>Если $y_2 = -2$, то $x_2 = 2(-2) - 2 = -4 - 2 = -6$.</p><p>Получаем две пары решений.</p><p>Ответ: $(2, 2)$, $(-6, -2)$.</p><p><strong>д)</strong> $ \begin{cases} 2x - y^2 = 5, \\ x + y^2 = 16. \end{cases} $</p><p>Решим систему методом сложения. Сложим первое и второе уравнения:</p><p>$(2x - y^2) + (x + y^2) = 5 + 16$</p><p>$3x = 21$</p><p>$x = 7$</p><p>Подставим найденное значение $x$ во второе уравнение системы:</p><p>$7 + y^2 = 16$</p><p>$y^2 = 16 - 7$</p><p>$y^2 = 9$</p><p>Отсюда $y_1 = 3$ и $y_2 = -3$.</p><p>Получаем две пары решений.</p><p>Ответ: $(7, 3)$, $(7, -3)$.</p><p><strong>е)</strong> $ \begin{cases} x^2 - 3y = -5, \\ x^2 - y = 1. \end{cases} $</p><p>Решим систему методом вычитания. Вычтем из первого уравнения второе:</p><p>$(x^2 - 3y) - (x^2 - y) = -5 - 1$</p><p>$x^2 - 3y - x^2 + y = -6$</p><p>$-2y = -6$</p><p>$y = 3$</p><p>Подставим найденное значение $y$ во второе уравнение системы:</p><p>$x^2 - 3 = 1$</p><p>$x^2 = 4$</p><p>Отсюда $x_1 = 2$ и $x_2 = -2$.</p><p>Получаем две пары решений.</p><p>Ответ: $(2, 3)$, $(-2, 3)$.</p>" ] #original: array:6 [ "id" => 1373823 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1148} "task" => array:2 [ "refs" => "209835" "type" => "task" ] "text" => "<p><strong>а)</strong> $ \begin{cases} x + y = 12, \\ xy = 32. \end{cases} $</p><p>Это система, которую удобно решить с помощью теоремы Виета для квадратного уравнения. Числа $x$ и $y$ являются корнями квадратного уравнения $t^2 - (x+y)t + xy = 0$.</p><p>Подставим значения из системы:</p><p>$t^2 - 12t + 32 = 0$</p><p>Решим это квадратное уравнение. Дискриминант $D = b^2 - 4ac = (-12)^2 - 4 \cdot 1 \cdot 32 = 144 - 128 = 16$.</p><p>Корни уравнения:</p><p>$t_1 = \frac{-b + \sqrt{D}}{2a} = \frac{12 + \sqrt{16}}{2} = \frac{12 + 4}{2} = \frac{16}{2} = 8$</p><p>$t_2 = \frac{-b - \sqrt{D}}{2a} = \frac{12 - \sqrt{16}}{2} = \frac{12 - 4}{2} = \frac{8}{2} = 4$</p><p>Таким образом, пары решений $(x, y)$ — это $(8, 4)$ и $(4, 8)$.</p><p>Ответ: $(4, 8)$, $(8, 4)$.</p><p><strong>б)</strong> $ \begin{cases} x - y = 4, \\ xy = 12. \end{cases} $</p><p>Воспользуемся методом подстановки. Выразим $x$ из первого уравнения:</p><p>$x = 4 + y$</p><p>Подставим это выражение во второе уравнение:</p><p>$(4 + y)y = 12$</p><p>$4y + y^2 = 12$</p><p>$y^2 + 4y - 12 = 0$</p><p>Решим полученное квадратное уравнение. По теореме Виета, корни $y_1 = -6$ и $y_2 = 2$.</p><p>Найдем соответствующие значения $x$:</p><p>Если $y_1 = -6$, то $x_1 = 4 + (-6) = -2$.</p><p>Если $y_2 = 2$, то $x_2 = 4 + 2 = 6$.</p><p>Получаем две пары решений.</p><p>Ответ: $(-2, -6)$, $(6, 2)$.</p><p><strong>в)</strong> $ \begin{cases} y = x + 2, \\ 4y + x^2 = 8. \end{cases} $</p><p>Используем метод подстановки. Подставим выражение для $y$ из первого уравнения во второе:</p><p>$4(x + 2) + x^2 = 8$</p><p>$4x + 8 + x^2 = 8$</p><p>$x^2 + 4x = 0$</p><p>Вынесем $x$ за скобки:</p><p>$x(x + 4) = 0$</p><p>Отсюда $x_1 = 0$ или $x_2 = -4$.</p><p>Найдем соответствующие значения $y$:</p><p>Если $x_1 = 0$, то $y_1 = 0 + 2 = 2$.</p><p>Если $x_2 = -4$, то $y_2 = -4 + 2 = -2$.</p><p>Получаем две пары решений.</p><p>Ответ: $(0, 2)$, $(-4, -2)$.</p><p><strong>г)</strong> $ \begin{cases} y^2 + 2x - 4y = 0, \\ 2y - x = 2. \end{cases} $</p><p>Применим метод подстановки. Выразим $x$ из второго уравнения:</p><p>$x = 2y - 2$</p><p>Подставим это выражение в первое уравнение:</p><p>$y^2 + 2(2y - 2) - 4y = 0$</p><p>$y^2 + 4y - 4 - 4y = 0$</p><p>$y^2 - 4 = 0$</p><p>$(y - 2)(y + 2) = 0$</p><p>Отсюда $y_1 = 2$ или $y_2 = -2$.</p><p>Найдем соответствующие значения $x$:</p><p>Если $y_1 = 2$, то $x_1 = 2(2) - 2 = 4 - 2 = 2$.</p><p>Если $y_2 = -2$, то $x_2 = 2(-2) - 2 = -4 - 2 = -6$.</p><p>Получаем две пары решений.</p><p>Ответ: $(2, 2)$, $(-6, -2)$.</p><p><strong>д)</strong> $ \begin{cases} 2x - y^2 = 5, \\ x + y^2 = 16. \end{cases} $</p><p>Решим систему методом сложения. Сложим первое и второе уравнения:</p><p>$(2x - y^2) + (x + y^2) = 5 + 16$</p><p>$3x = 21$</p><p>$x = 7$</p><p>Подставим найденное значение $x$ во второе уравнение системы:</p><p>$7 + y^2 = 16$</p><p>$y^2 = 16 - 7$</p><p>$y^2 = 9$</p><p>Отсюда $y_1 = 3$ и $y_2 = -3$.</p><p>Получаем две пары решений.</p><p>Ответ: $(7, 3)$, $(7, -3)$.</p><p><strong>е)</strong> $ \begin{cases} x^2 - 3y = -5, \\ x^2 - y = 1. \end{cases} $</p><p>Решим систему методом вычитания. Вычтем из первого уравнения второе:</p><p>$(x^2 - 3y) - (x^2 - y) = -5 - 1$</p><p>$x^2 - 3y - x^2 + y = -6$</p><p>$-2y = -6$</p><p>$y = 3$</p><p>Подставим найденное значение $y$ во второе уравнение системы:</p><p>$x^2 - 3 = 1$</p><p>$x^2 = 4$</p><p>Отсюда $x_1 = 2$ и $x_2 = -2$.</p><p>Получаем две пары решений.</p><p>Ответ: $(2, 3)$, $(-2, 3)$.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "209836" "type" => "task" ] "previous" => array:2 [ "refs" => "209834" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1113 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1116 #items: 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№655 (с. 202)
Условие. №655 (с. 202)
скриншот условия
655 Решите систему уравнений:
а) $\begin{cases} x+y=12 \\ xy=32 \end{cases}$
б) $\begin{cases} x-y=4 \\ xy=12 \end{cases}$
в) $\begin{cases} y=x+2 \\ 4y+x^2=8 \end{cases}$
г) $\begin{cases} y^2+2x-4y=0 \\ 2y-x=2 \end{cases}$
д) $\begin{cases} 2x-y^2=5 \\ x+y^2=16 \end{cases}$
е) $\begin{cases} x^2-3y=-5 \\ x^2-y=1 \end{cases}$
Решение 1. №655 (с. 202)
Решение 2. №655 (с. 202)
Решение 3. №655 (с. 202)
Решение 4. №655 (с. 202)
а) $ \begin{cases} x + y = 12, \\ xy = 32. \end{cases} $
Это система, которую удобно решить с помощью теоремы Виета для квадратного уравнения. Числа $x$ и $y$ являются корнями квадратного уравнения $t^2 - (x+y)t + xy = 0$.
Подставим значения из системы:
$t^2 - 12t + 32 = 0$
Решим это квадратное уравнение. Дискриминант $D = b^2 - 4ac = (-12)^2 - 4 \cdot 1 \cdot 32 = 144 - 128 = 16$.
Корни уравнения:
$t_1 = \frac{-b + \sqrt{D}}{2a} = \frac{12 + \sqrt{16}}{2} = \frac{12 + 4}{2} = \frac{16}{2} = 8$
$t_2 = \frac{-b - \sqrt{D}}{2a} = \frac{12 - \sqrt{16}}{2} = \frac{12 - 4}{2} = \frac{8}{2} = 4$
Таким образом, пары решений $(x, y)$ — это $(8, 4)$ и $(4, 8)$.
Ответ: $(4, 8)$, $(8, 4)$.
б) $ \begin{cases} x - y = 4, \\ xy = 12. \end{cases} $
Воспользуемся методом подстановки. Выразим $x$ из первого уравнения:
$x = 4 + y$
Подставим это выражение во второе уравнение:
$(4 + y)y = 12$
$4y + y^2 = 12$
$y^2 + 4y - 12 = 0$
Решим полученное квадратное уравнение. По теореме Виета, корни $y_1 = -6$ и $y_2 = 2$.
Найдем соответствующие значения $x$:
Если $y_1 = -6$, то $x_1 = 4 + (-6) = -2$.
Если $y_2 = 2$, то $x_2 = 4 + 2 = 6$.
Получаем две пары решений.
Ответ: $(-2, -6)$, $(6, 2)$.
в) $ \begin{cases} y = x + 2, \\ 4y + x^2 = 8. \end{cases} $
Используем метод подстановки. Подставим выражение для $y$ из первого уравнения во второе:
$4(x + 2) + x^2 = 8$
$4x + 8 + x^2 = 8$
$x^2 + 4x = 0$
Вынесем $x$ за скобки:
$x(x + 4) = 0$
Отсюда $x_1 = 0$ или $x_2 = -4$.
Найдем соответствующие значения $y$:
Если $x_1 = 0$, то $y_1 = 0 + 2 = 2$.
Если $x_2 = -4$, то $y_2 = -4 + 2 = -2$.
Получаем две пары решений.
Ответ: $(0, 2)$, $(-4, -2)$.
г) $ \begin{cases} y^2 + 2x - 4y = 0, \\ 2y - x = 2. \end{cases} $
Применим метод подстановки. Выразим $x$ из второго уравнения:
$x = 2y - 2$
Подставим это выражение в первое уравнение:
$y^2 + 2(2y - 2) - 4y = 0$
$y^2 + 4y - 4 - 4y = 0$
$y^2 - 4 = 0$
$(y - 2)(y + 2) = 0$
Отсюда $y_1 = 2$ или $y_2 = -2$.
Найдем соответствующие значения $x$:
Если $y_1 = 2$, то $x_1 = 2(2) - 2 = 4 - 2 = 2$.
Если $y_2 = -2$, то $x_2 = 2(-2) - 2 = -4 - 2 = -6$.
Получаем две пары решений.
Ответ: $(2, 2)$, $(-6, -2)$.
д) $ \begin{cases} 2x - y^2 = 5, \\ x + y^2 = 16. \end{cases} $
Решим систему методом сложения. Сложим первое и второе уравнения:
$(2x - y^2) + (x + y^2) = 5 + 16$
$3x = 21$
$x = 7$
Подставим найденное значение $x$ во второе уравнение системы:
$7 + y^2 = 16$
$y^2 = 16 - 7$
$y^2 = 9$
Отсюда $y_1 = 3$ и $y_2 = -3$.
Получаем две пары решений.
Ответ: $(7, 3)$, $(7, -3)$.
е) $ \begin{cases} x^2 - 3y = -5, \\ x^2 - y = 1. \end{cases} $
Решим систему методом вычитания. Вычтем из первого уравнения второе:
$(x^2 - 3y) - (x^2 - y) = -5 - 1$
$x^2 - 3y - x^2 + y = -6$
$-2y = -6$
$y = 3$
Подставим найденное значение $y$ во второе уравнение системы:
$x^2 - 3 = 1$
$x^2 = 4$
Отсюда $x_1 = 2$ и $x_2 = -2$.
Получаем две пары решений.
Ответ: $(2, 3)$, $(-2, 3)$.
Другие задания:
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