# How do you solve the following system: y = 3x – 12, 2x-3y=-13?

Dec 18, 2015

$\textcolor{w h i t e}{\times} x = 7$ and $y = 9$

#### Explanation:

$\textcolor{w h i t e}{\times} y = 3 x - 12 , 2 x - 3 y = - 13$

$\textcolor{w h i t e}{\times} 2 x - 3 y = - 13 \iff y = \frac{2 x + 13}{3}$

$\implies \textcolor{red}{3 x - 12} = \frac{2 x + 13}{3}$
$\implies \textcolor{red}{3 \times} \left(3 x - 12\right) = \textcolor{red}{3 \times} \frac{2 x + 13}{3}$
$\implies 9 x - 36 \textcolor{red}{- 2 x + 36} = 2 x + 13 \textcolor{red}{- 2 x + 36}$
$\implies \textcolor{red}{\frac{1}{7} \times} 7 x = \textcolor{red}{\frac{1}{7} \times} 49$
$\implies x = 7$

$\textcolor{w h i t e}{\times} y = 3 x - 12$
$\textcolor{w h i t e}{\times x} = 3 \times \textcolor{red}{7} - 12$
$\textcolor{w h i t e}{\times x} = 9$