# How do you solve the following system?:  x +2y =-7 , -2x +2y = 4

Jun 6, 2018

$x = \frac{11}{3}$

$y = - \frac{5}{3}$

#### Explanation:

$x + 2 y = - 7 \text{ } \left(1\right)$

$- 2 x + 2 y = 4 \text{ } \left(2\right)$

Subtract equation $\left(1\right)$ from $\left(2\right)$

$- 3 x = 11$

$x = - \frac{11}{3}$

Substitute $x = - \frac{11}{3}$ into equation $\left(1\right)$

$- \frac{11}{3} + 2 y = - 7$

$2 y = \frac{11}{3} - 7$

$2 y = - \frac{10}{3}$

$y = - \frac{5}{3}$