# How do you solve the following system: -x+6y=12, x-4y=2 ?

Dec 14, 2015

$\textcolor{w h i t e}{\times} x = 30$, $y = 7$

#### Explanation:

$\textcolor{w h i t e}{\times} - x + 6 y = 12 , x - 4 y = 2$

$\textcolor{w h i t e}{\times} - x + 6 y = 12 \iff y = \frac{x + 12}{6}$
$\textcolor{w h i t e}{\times} x - 4 y = 2 \iff y = \frac{x - 2}{4}$

$\textcolor{w h i t e}{\times} y = \frac{x + 12}{6}$
$\implies \textcolor{b l u e}{\frac{x - 2}{4}} = \frac{x + 12}{6}$

Multiply both side by $\textcolor{red}{12}$:
$\textcolor{w h i t e}{\times} \textcolor{red}{12 \times} \frac{x - 2}{4} = \textcolor{red}{12 \times} \frac{x + 12}{6}$
$\implies 3 x - 6 = 2 x + 24$

Add $\textcolor{red}{- 2 x + 6}$ to both side:
$\textcolor{w h i t e}{\times} 3 x - 6 \textcolor{red}{- 2 x + 6} = 2 x + 24 \textcolor{red}{- 2 x + 6}$

$\textcolor{w h i t e}{\times} x = 30$

$\textcolor{w h i t e}{\times} y = \frac{x - 2}{4}$

$\textcolor{w h i t e}{\times x} = \frac{\textcolor{red}{30} - 2}{4}$
$\textcolor{w h i t e}{\times x} = \frac{\textcolor{red}{28}}{4}$
$\textcolor{w h i t e}{\times x} = 7$