Question

решите систему уравнений с двумя переменными:
1){3x-y=11
{4x+y=22
2){5x=31-8y
{3x+8y=25

Answer 1

$3x - y = 11 \\ 4x + y = 22 \\ . \\ 4x + y + 3x - y = 22 + 11 \\ 4x + y = 22 \\ . \\ 7x = 33 \\ 4x + y = 22 \\ . \\ x = \frac{33}{7} \\ y = 22 - 4 \times \frac{33}{7} \\ . \\ x = \frac{7}{33} \\ y = - \frac{55}{7}$

2)

$5x = 31 - 8y \\ 3x + 8y = 25 \\ . \\ 5x + 8y = 31 \\ 3x + 8y = 25 \\ . \\ 5x + 8y = 31 \\ - 3x - 8y + 5x + 8y = 31 - 25 \\ . \\ 5x + 8y = 31 \\ 2x = 6 \\ . \\ 5x + 8y = 31 \\ x = 3 \\ . \\ 8y = 31 - 15 \\ x = 3 \\ . \\ y = 2 \\ x = 3$