# How do you solve the following system?:  -x-8y=32, y= 1/2x +2

Nov 21, 2015

$\left(x , y\right) = \left(- \frac{48}{5} , - \frac{14}{5}\right)$

#### Explanation:

[1]$\textcolor{w h i t e}{\text{XXX}} - x - 8 y = 32$
[2]$\textcolor{w h i t e}{\text{XXX}} y = \frac{1}{2} x + 2$

Substitute $\left(\frac{1}{2} x + 2\right)$ from [2] for $y$ in [1]
[3]$\textcolor{w h i t e}{\text{XXX}} - x - 8 \left(\frac{1}{2} x + 2\right) = 32$

Simplify
[4]$\textcolor{w h i t e}{\text{XXX}} - x - 4 x - 16 = 32$

[5]$\textcolor{w h i t e}{\text{XXX}} - 5 x = 48$

[6]$\textcolor{w h i t e}{\text{XXX}} x = - \frac{48}{5}$

Substitute $\left(- \frac{48}{5}\right)$ from [6] for $x$ in [2]
[7]$\textcolor{w h i t e}{\text{XXX}} y = \frac{1}{2} \left(- \frac{48}{5}\right) + 2$

Simplify
[8]$\textcolor{w h i t e}{\text{XXX}} y = - \frac{14}{5}$