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2. Решить системы способом сложения:{2х — у = 5, 2x +7y = 11.​ Смотреть ответ Участник Знаний Участник Знаний Ответ: (2,875;0,75) Пошаговое объяснение: {2х-у=5. |×(-1) {2х+7у=11 {-2х+у=-5 {2х+7у=11 Метод алгебраического сложения 8у=6 у=6/8 у=0,75 Подставляем значение у в одно из уравнений 2х-у=5 2х-0,75=5 2х=5+0,75 2х=5,75 х=5,75/2 х=2,875 Новые вопросы в Математика У млині було 830 кг борошна. Продали 6 пакетів по 5 кг муки і ще мішок муки вагою 100 кг. Скільки кілограмів борошна залишилося в млині? побудуйте точки та виміряйте довжину відрізка з кінця в даних точках А (-2;2) Р(2;-1)дам 100 балів ​ У магазин завезли 280 білих троянд, що становить 4/5 від кількості рожевих. Після того, як частину продали, лишилося 120 троянд. Скільки троянд продал … и? 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Answer 1

Система уравнений: $\begin{cases} 2x - y = 5 \\ 2x + 7y = 11 \end{cases}$

Давайте сложим оба уравнения, чтобы избавиться от переменной x:

$(2x - y) + (2x + 7y) = 5 + 11$

$4x + 6y = 16$

Теперь выразим x:

$4x = 16 - 6y$

$x = \frac{16 - 6y}{4}$

$x = 4 - \frac{3y}{2}$

Теперь подставим это обратно в любое из исходных уравнений, например, в первое:

$2(4 - \frac{3y}{2}) - y = 5$

$8 - 3y - y = 5$

$8 - 4y = 5$

$-4y = 5 - 8$

$-4y = -3$

$y = \frac{-3}{-4} = \frac{3}{4} = 0.75$

Теперь найдем значение x, подставив y обратно в любое из уравнений:

$2x - 0.75 = 5$

$2x = 5 + 0.75$

$2x = 5.75$

$x = \frac{5.75}{2} = 2.875$

Таким образом, решение системы уравнений равно $x = 2.875$ и $y = 0.75$. Поэтому ответ верен.