# How do you solve the system x+6y=-22 and  -6x-2y=-4 by substitution?

Jun 10, 2015

The solution for the system of equations is
 color(red)(x = 2 , y=-4

#### Explanation:

$x + 6 y = - 22$
x=color(red)(-22 - 6y ..................equation $\left(1\right)$
$- 6 x - 2 y = - 4$ ............equation $\left(2\right)$

Substituting equation $\left(1\right)$ in equation $\left(2\right)$ to find $y$

$- 6 x - 2 y = - 4$
$- 6 \textcolor{red}{\left(- 22 - 6 y\right)} - 2 y = - 4$
$132 + 36 y - 2 y = - 4$
$132 + 34 y = - 4$
$34 y = - 136$
color(red)(y=-4

Substituting $y$ in equation $1$ to find $x$
$x = - 22 - 6 y$
$x = - 22 - 6. \left(- 4\right)$
$x = - 22 + 24$
 color(red)(x = 2