Question

ДОПОМОЖІТЬ БУДЬ ЛАСКА!!!!!!!!! РОЗВЯЗАТИ СИСТЕМУ РІВНЯНЬ ТРЬОМА СПОСОБАМИ{х+2у=5{3х-2у=11​ Смотреть ответ PR0stoV1ad PR0stoV1ad Ответ: 1) {x = 5 - 2y {15 - 6y - 2y = 11 {x = 5 - 2y {-8y = -4 {x = 5 - 2y {y = 0.5 {x = 4 {y = 0.4 2) {x + 2y = 5 + {3x - 2y = 11 ---------------- 4x = 16 x = 4 4 + 2y = 5 2y = 1 y = 0.5 {x = 4 {y = 0.5 Новые вопросы в Алгебра еще два вопросика, отдам последнии баллы(( (2a–2b)^2/a–b; (3c+9d)^2/c+3d; (3x+6y)^2/5x+10y; 4x^2–y^2/10x+5y a^8+a^5/a^5+a^2 при a=–1/2; b^10–b^8/b^8–b^6 приb=–0,1 Виконай ділення 0,6х4yс : 0,2x3y Виберіть одну відповідь: 3хус 0,3хс 0,4хус 3хс Визнач значення змінної, при якому дріб (6 + y) : (y – 1) перетворюється на нуль Виберіть одну відповідь: y = 6 y = 1 y = –6 y = –1 Предыдущий Следующий Вместе мы знаем больше Этот сайт использует cookies Политика Cookies . Вы можете указать условия хранения и доступ к cookies в своем браузере. 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Answer 1

Розглянемо способи розв'язання системи рівнянь:

Система рівнянь:

1. x + 2y = 5
2. 3x - 2y = 11

Спосіб 1: Метод заміщення

Можна використовувати метод заміщення, щоб розв'язати цю систему. Давайте спробуємо виразити одну змінну через іншу і підставимо це значення у інше рівняння.

З рівняння (1) виразимо x: x = 5 - 2y

Підставимо це значення x у рівняння (2): 3(5 - 2y) - 2y = 11

Розв'яжемо це рівняння для y: 15 - 6y - 2y = 11 -8y = 11 - 15 -8y = -4

Тепер розв'яжемо для y: y = (-4) / (-8) y = 0.5

Тепер ми знаємо значення y, і ми можемо знайти x, використовуючи рівняння (1): x = 5 - 2y x = 5 - 2(0.5) x = 5 - 1 x = 4

Отже, розв'язок системи рівнянь: x = 4 y = 0.5

Спосіб 2: Метод додавання

Також можна використовувати метод додавання, щоб розв'язати цю систему. Додамо обидва рівняння так, щоб позбутися однієї змінної.

Рівняння (1) + Рівняння (2): (x + 2y) + (3x - 2y) = 5 + 11

Спростимо вираз: 4x = 16

Розділимо обидва боки на 4, щоб знайти x: x = 16 / 4 x = 4

Тепер, ми можемо підставити значення x у рівняння (1) для знаходження y: x + 2y = 5 4 + 2y = 5

Віднімемо 4 від обох боків: 2y = 5 - 4 2y = 1

Розділимо обидва боки на 2, щоб знайти y: y = 1 / 2 y = 0.5

Отже, розв'язок системи рівнянь такий же: x = 4 і y = 0.5.

Спосіб 3: Матричний метод

Систему рівнянь також можна розв'язати матричним методом, представляючи її у вигляді матриці. Матричний метод виглядає наступним чином:

Матриця коефіцієнтів (A) та вектор-стовпчик вільних членів (B): A = | 1 2 | | 3 -2 |

B = | 5 | | 11 |

Тепер знайдемо обернену матрицю A^(-1): A^(-1) = (1 / det(A)) * | -2 -2 | | -3 1 |

Спростимо детермінант det(A): det(A) = 1*(-2) - 3*2 = -2 - 6 = -8

Тепер знайдемо обернену матрицю: A^(-1) = (1 / (-8)) * | -2 -2 | | -3 1 |

A^(-1) = | 1/4 1/4 | | 3/8 -1/8 |

Тепер, ми можемо знайти вектор розв'язку X, помножив обернену матрицю на вектор B: X = A^(-1) * B X = | 1/4 1/4 | * | 5 | | 11 |

X = | (1/4)*5 + (1/4)*11 | | (3/8)*5 - (1/8)*11 |

X = | (5/4) + (11/4) | | (15/8) - (11/8) |

X = | 16/4 | | 4/8 |

X = | 4 | | 0.5 |

Отже, розв'язок системи рівнянь такий же: x = 4 і y = 0.5.

Отже, ми отримали однакові результати для x і y за допомогою трьох різних методів розв'язання системи рівнянь.