# How do you solve the following system?:  2x + 7y = -8, x - 2y = 7

Apr 21, 2018

$x = 3$ and $y = - 2$

#### Explanation:

2x + 7y = -8 color(white)(....) ——(1)
x - 2y = 7 color(white)(....) ——(2)

Multiply second equation by $2$
2x - 4y = 14 color(white)(....) ——(3)

Subtract $3$nd equation from $1$st

$2 x + 7 y - \left(2 x - 4 y\right) = - 8 - 14$

$2 x + 7 y - 2 x + 4 y = - 22$

$11 y = - 22$

$y = - \frac{22}{11}$

$y = - 2$

Substitute $y = - 2$ in equation $\left(1\right)$

2x + (7 × -2) = -8

$2 x - 14 = - 8$

$2 x = 14 - 8$

$2 x = 6$

$x = \frac{6}{2}$

$x = 3$