# How do you solve the following system?: -2x -2y =1, 2x -y = -2

Apr 24, 2018

$x = - \frac{5}{6}$
$y = \frac{1}{3}$

#### Explanation:

Given -

$- 2 x - 2 y = 1$ -----------(1)
$2 x - y = - 2$--------------(2)

Solve equation (2) for $y$

$- y = - 2 - 2 x$

Multiply both sides by $- 1$

$y = 2 + 2 x$

Substitute $y = 2 + 2 x$ in equation (1)

$- 2 x - 2 \left(2 + 2 x\right) = 1$

$- 2 x - 4 - 4 x = 1$

$- 4 - 6 x = 1$

$- 6 x = 1 + 4 = 5$

$x = - \frac{5}{6}$

Substitute $x = \frac{5}{6}$in equation (2)

$2 \left(- \frac{5}{6}\right) - y = - 2$

$- \frac{5}{3} - y = - 2$

$- y = - 2 + \frac{5}{3} = \frac{- 6 + 5}{3} = - \frac{1}{3}$

$- y = - \frac{1}{3}$

$y = \frac{1}{3}$