Question

Решить систему: а)методом подстановки б)методом сложения {х+2y=7 {5х-y=2 Смотреть ответ Zombynella Zombynella Ответ: а)Решение системы уравнений  х=1                                                         у=3 б)Решение системы уравнений  х=1                                                          у=3 Объяснение: Решить систему: а)методом подстановки {х+2y=7 {5х-y=2 Выразим х через у в первом уравнении, подставим выражение во второе уравнение и вычислим у: х=7-2у 5(7-2у)-у=2 35-10у-у=2 -11у=2-35 -11у= -33 у= -33/-11 у=3 х=7-2у х=7-2*3 х=1 Решение системы уравнений  х=1                                                       у=3 б)методом сложения {х+2y=7 {5х-y=2 Смысл метода алгебраического сложения в том, чтобы при сложении уравнений одно неизвестное взаимно уничтожилось. То есть, чтобы коэффициенты при неизвестном каком-то были одинаковыми, но с противоположными знаками. Для того, чтобы этого добиться, преобразовывают уравнения, можно умножать обе части уравнения на одно и то же число, делить.   В данной системе нужно первое уравнение умножить на -5: -5х-10у= -35  5х-y=2 Складываем уравнения: -5х+5х-10у-у= -35+2 -11у= -33 у= -33/-11 у=3 Теперь значение у подставляем в любое из двух уравнений системы и вычисляем х: х+2y=7 х=7-2*3 х=1 Решение системы уравнений  х=1                                                       у=3 Новые вопросы в Алгебра помогите пожалуйста обчислить.там если что в начале 3⁶заранее спасибо ​ Здравствуйте друзья ! Помогите пожалуйста с Алгеброй! Решите уравнение (x²+x)²+2(x²+x)-8=0​ Обчисліть 30+3+(3-²)³пожалуйста ​ Здравствуйте друзья! Помогите пожалуйста с Алгеброй!15 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

Кажется, вы уже решили данную систему уравнений. Ваш ответ верен. Чтобы подтвердить, вот решение системы уравнений:

а) Метод подстановки: Исходные уравнения:

1. $x + 2y = 7$
2. $5x - y = 2$

Из первого уравнения выразим $x$: $x = 7 - 2y$

Подставим выражение для $x$ во второе уравнение: $5(7 - 2y) - y = 2$

Упростим: $35 - 10y - y = 2$ $-11y = -33$ $y = 3$

Теперь подставим значение $y$ в выражение для $x$: $x = 7 - 2 \cdot 3 = 1$

Итак, решение методом подстановки: $x = 1$, $y = 3$.

б) Метод сложения: Исходные уравнения:

1. $x + 2y = 7$
2. $5x - y = 2$

Для алгебраического сложения умножим первое уравнение на -5: $-5x - 10y = -35$

Сложим полученное уравнение с вторым уравнением: $-5x - 10y + 5x - y = -35 + 2$ $-11y = -33$ $y = 3$

Подставим значение $y$ в первое уравнение: $x + 2 \cdot 3 = 7$ $x + 6 = 7$ $x = 1$

Итак, решение методом сложения также дает нам $x = 1$, $y = 3$.

Оба метода приводят к одинаковому результату: $x = 1$, $y = 3$. Ваш ответ верный.