Question

Система способом додавання{5х+7у=8{10х-7у=17(це одна система, допоможіть будь ласка)​ Посмотреть ответы mrx5835 mrx5835 Ответ:X = 49/30; y= -1/21Объяснение:Решим эту систему методом сложения. Для этого умножим первое уравнение на 2 и сложим со вторым уравнением:\begin{cases} 10x + 14y = 16 \\ 10x - 7y = 17 \end{cases}Теперь избавимся от неизвестной x. Для этого вычтем из первого уравнения второе:\begin{cases} 21y = -1 \\ 10x - 7y = 17 \end{cases}Разделим оба уравнения на 21:\begin{cases} y = -\frac{1}{21} \\ 10x - 7y = 17 \end{cases}Подставим значение y во второе уравнение:10x - 7 \cdot \left(-\frac{1}{21}\right) = 1710x + \frac{7}{21} = 1710x = \frac{350}{21} - \frac{7}{21}10x = \frac{343}{21}x = \frac{343}{210}Ответ: x = 49/30; y = -1/21. Yasyko Yasyko Ответ: x = -26   y = -21Объяснение:{ 5x + 7y = 8  | -2  10x - 7y = 17{ -10x - 14y = -16   10x - 7y = 17-21y = 1y = -21x = (17 - 147) : 10x = 13

Answer 1

Solving the System of Equations

To solve the system of equations 5x + 7y = 8 and 10x - 7y = 17, we can use the method of addition.

First, let's multiply the first equation by 2 and add it to the second equation:

2 * (5x + 7y) = 2 * 8
10x + 14y = 16

10x + 14y + (10x - 7y) = 16 + 17
10x + 14y + 10x - 7y = 33
20x + 7y = 33

Now, let's eliminate the variable x by subtracting the second equation from the first equation:

(20x + 7y) - (10x - 7y) = 33 - 17
20x + 7y - 10x + 7y = 16
10x + 14y = 16

We now have a new system of equations:

10x + 14y = 16   ---(1)
10x + 14y = 16   ---(2)

Since the two equations are identical, we can conclude that the system of equations is dependent and has infinitely many solutions. This means that any values of x and y that satisfy one equation will also satisfy the other equation.

Therefore, we cannot determine a unique solution for the system of equations 5x + 7y = 8 and 10x - 7y = 17.