# How do you solve 4x+2y=-8 and -2x+3y=12?

May 16, 2018

$\left(x , y\right) = \left(- 3 , 2\right)$

#### Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} 4 x + 2 y = - 8$
[2]$\textcolor{w h i t e}{\text{XXX}} - 2 x + 3 y = 12$

Multiplying [2] by $2$ so the coefficient of $x$ has the same magnitude as that of [1]
[3]$\textcolor{w h i t e}{\text{XXX}} - 4 x + 6 y = 24$

[4]$\textcolor{w h i t e}{\text{XXX}} 8 y = 16$
[5]$\textcolor{w h i t e}{\text{XXX}} y = 2$
Substituting $2$ for $y$ in [1]
[6]$\textcolor{w h i t e}{\text{XXX}} 4 x + 2 \cdot 2 = - 8$
[7]$\textcolor{w h i t e}{\text{XXX}} x = - 3$