# How do you solve the following system: 2x-6y=-12 , 3x -2y=24 ?

Dec 15, 2015

$\textcolor{w h i t e}{\times} x = 12$ and $y = 6$

#### Explanation:

$\textcolor{w h i t e}{\times} 2 x - 6 y = - 12$, $3 x - 2 y = 24$

$\left\{\begin{matrix}2 x - 6 y = - 12 \iff y = \frac{x + 6}{3} \\ 3 x - 2 y = 24 \iff y = \frac{3 x - 24}{2}\end{matrix}\right.$

$\textcolor{w h i t e}{\times} y = \frac{x + 6}{3}$
$\implies \textcolor{red}{\frac{3 x - 24}{2}} = \frac{x + 6}{3}$

Multiply both sides by $\textcolor{red}{6}$:
$\textcolor{w h i t e}{\times} \textcolor{red}{6 \times} \frac{3 x - 24}{2} = \textcolor{red}{6 \times} \frac{x + 6}{3}$
$\implies 9 x - 72 = 2 x + 12$

Add $\textcolor{red}{- 2 x + 72}$ to both sides:
$\textcolor{w h i t e}{\times} 9 x - 72 \textcolor{red}{- 2 x + 72} = 2 x + 12 \textcolor{red}{- 2 x + 72}$
$\implies 7 x = 84$

Multiply both sides by $\textcolor{red}{\frac{1}{7}}$:
$\textcolor{w h i t e}{\times} \textcolor{red}{\frac{1}{7} \times} 7 x = \textcolor{red}{\frac{1}{7} \times} 84$
$\implies x = 12$

$\textcolor{w h i t e}{\times} y = \frac{x + 6}{3}$
$\textcolor{w h i t e}{\times x} = \frac{\textcolor{red}{12} + 6}{3}$
$\textcolor{w h i t e}{\times x} = 6$