# How do you solve the following system: y = 3x – 12, 2x – 4y = 8?

Dec 30, 2015

$x = 4$, $y = 0$

#### Explanation:

$\textcolor{w h i t e}{\times} y = 3 x - 12 , 2 x - 4 y = 8$

$\textcolor{w h i t e}{\times} 2 x - 4 y = 8 \iff y = \frac{x - 4}{2}$

$\implies \textcolor{red}{3 x - 12} = \frac{x - 4}{2}$
$\implies \textcolor{b l u e}{x - 4} = \frac{x - 4}{2}$

$\implies x - 4 = 0$
$\implies x - 4 \textcolor{g r e e n}{+ 4} = 0 \textcolor{g r e e n}{+ 4}$
$\implies x = 4$

$\implies y = \frac{\textcolor{red}{4} - 4}{2}$
$\implies y = 0$