# How do you solve the following system?:  -8x+3y=12 , -2x + 6y = -8

Mar 15, 2016

$x = - \frac{16}{7}$

$y = - \frac{44}{21}$

#### Explanation:

$\textcolor{red}{2} \cdot \left(- 8 x + 3 y\right) = \textcolor{red}{2} \cdot 12$
$- 16 x + \textcolor{b l u e}{6 y} = 24$
$\textcolor{b l u e}{6 y} = 24 + 16 x$

$- 2 x + \textcolor{b l u e}{6 y} = - 8 \text{ } \left(1\right)$
$- 2 x + 24 + 16 x = - 8$
$14 x = - 8 - 24$
$14 x = - 32$
$x = - \frac{32}{14}$
$x = - \frac{16}{7}$
$\text{use (1)}$
$- 2 \left(- \frac{16}{7}\right) + 6 y = - 8$
$\frac{32}{7} + 6 y = - 8$
$6 y = - 8 - \frac{32}{7}$
$6 y = \frac{- 56 - 32}{7}$
$y = - \frac{88}{42}$

$y = - \frac{44}{21}$