# How do you solve the following system of equations?: -x – 2y = 12 , 12x+y=8?

Dec 13, 2015

(28/23 , -152/28)#

#### Explanation:

$\left\{\begin{matrix}- x - 2 y = 12 \\ 12 x + y = 8\end{matrix}\right.$

Multiply the first equation by 2, to eliminate $y$

$\left\{\begin{matrix}- x - 2 y = 12 \\ \textcolor{red}{2} \cdot \left(12 x + y = 8\right)\end{matrix}\right.$

$\implies \left\{\begin{matrix}- x - 2 y = 12 \\ 24 x + 2 y = 16\end{matrix}\right.$

$\implies \left\{\begin{matrix}- x \cancel{- 2 y} = 12 \\ 24 x \cancel{+ 2 y} = 16\end{matrix}\right.$

$\implies 23 x = 28$

$\implies \frac{13 x}{23} = \frac{28}{23} \implies x = \frac{28}{23}$

Substitute $x = \frac{28}{23}$ into one of the original equation to solve for $y$

We will use this one $12 x + y = 8$

$12 \left(\frac{28}{23}\right) + y = 8$

$\frac{336}{23} + y = \frac{184}{23}$

$y = \frac{184}{23} - \frac{336}{23}$

$y = - \frac{152}{23}$

Answer :$\left(\frac{28}{23} , - \frac{152}{28}\right)$