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

Feb 4, 2016

$\left(x , y\right) = \left(\frac{18}{7} , \frac{20}{7}\right)$

#### Explanation:

Given:
[1]$\textcolor{w h i t e}{\text{XXX}} 2 x - 6 y = - 12$
[2]$\textcolor{w h i t e}{\text{XXX}} 2 x + y = 8$

Subtract equation [1] from equation [2] to get:
[3]$\textcolor{w h i t e}{\text{XXX}} 7 y = 20$

Divide both sides of equation [3] by $7$:
[4]$\textcolor{w h i t e}{\text{XXX}} y = \frac{20}{7}$

Substitute $\frac{20}{7}$, the value given for $y$ in equation [4], for $y$ in equation [2]
[5]$\textcolor{w h i t e}{\text{XXX}} 2 x + \frac{20}{7} = 8$

Subtract $\frac{20}{7}$ from both sides of equation [5] and simplify the right side
[6]$\textcolor{w h i t e}{\text{XXX}} 2 x = 8 - \frac{20}{7} = \frac{56}{7} - \frac{20}{7} = \frac{36}{7}$

Divide both sides of equation [6] by $2$
$\textcolor{w h i t e}{\text{XXX}} x = \frac{18}{7}$