Question

4x-8y=31 7x+8y=19 способом сложения

Answer 1

4x - 8y = 31

7x + 8y = 19

Сложим левую часть первого уравнения с левой частью второго уравнения, то же самое с правыми:

(4x - 8y) + (7x + 8y) = 31 + 19

4x - 8y + 7x + 8y = 50

11х = 50

х = 50/11

Выразим у из первого уравнения. Поделим обе части на 8:

4x - 8y = 31

1/2х - у = 31/8

у = 1/2х - 31/8

Подставим значение х:

у = 1/2 × 50/11 - 31/8

у = 50/22 - 31/8

у = 200/88 - 341/88

у = -141/88

Ответ: (50/11; -141/88).

Answer 2

To solve the system of equations using the method of addition, we'll add the two equations together to eliminate the variable "y."

Here are the original equations:

1. 4x - 8y = 31
2. 7x + 8y = 19

When we add equation 1) and equation 2), the "y" terms cancel out: (4x - 8y) + (7x + 8y) = 31 + 19

Simplifying the equation: 4x + 7x - 8y + 8y = 50 11x = 50

Dividing both sides of the equation by 11: 11x/11 = 50/11 x = 50/11

Now that we have the value of "x," we can substitute it back into one of the original equations to solve for "y." Let's use equation 1):

4x - 8y = 31 4(50/11) - 8y = 31 200/11 - 8y = 31 -8y = 31 - 200/11 -8y = (341 - 200)/11 -8y = 141/11 y = (141/11) * (-1/8) y = -141/88

Therefore, the solution to the system of equations is: x = 50/11 y = -141/88