# How do you solve the following system?:  -2y=2x+6 , -x-8y=32

Mar 26, 2016

The solution for the system of equations is:
 color(blue)( x = 8/7
color(blue)(y = -29 / 7

#### Explanation:

$- 2 y = 2 x + 6$
$\textcolor{b l u e}{2 x} + 2 y = - 6$..........equation $\left(1\right)$

$- x - 8 y = 32$ , multiplying by $2$
$\textcolor{b l u e}{- 2 x} - 16 y = 64$ .....equation $\left(2\right)$

Solving by elimination:

Adding equations $1$ and $2$:

$\cancel{\textcolor{b l u e}{2 x}} + 2 y = - 6$
$\cancel{\textcolor{b l u e}{- 2 x}} - 16 y = 64$

$- 14 y = 58$

$y = \frac{58}{- 14}$

color(blue)(y = -29 / 7

Finding $x$ from equation $2$:
$- x - 8 y = 32$

$- 8 y - 32 = x$

$- 8 \cdot \textcolor{b l u e}{\left(\frac{29}{- 7}\right)} - 32 = x$

$\frac{232}{7} - 32 = x$

$\frac{232}{7} - \frac{224}{7} = x$

 color(blue)( x = 8/7

The solution for the system of equations is:
 color(blue)( x = 8/7
color(blue)(y = -29 / 7