# How do you solve the system of equations -x-y=15 and -8x+8y=24?

Aug 4, 2016

$\left\{\begin{matrix}x = - 9 \\ y = - 6\end{matrix}\right.$

#### Explanation:

The system of equations given to you looks like this

$\left\{\begin{matrix}- \textcolor{w h i t e}{1} x - \textcolor{w h i t e}{1} y = 15 \\ - 8 x + 8 y = 24\end{matrix}\right.$

Notice that one equation features $y$ with a positive sign and the other has it with a negative sign. This means that if you get the coefficients to match, you can add the two equations and get rid of the $y$ terms.

To do that, multiply the first equation by $8$

$\left\{\begin{matrix}- \textcolor{w h i t e}{1} x - \textcolor{w h i t e}{1} y = 15 \text{ } | \times 8 \\ - 8 x + 8 y = 24\end{matrix}\right.$

this will get you

$\left\{\begin{matrix}- 8 x - 8 y = 120 \\ - 8 x + 8 y = \textcolor{w h i t e}{1} 24\end{matrix}\right.$

$\left\{\begin{matrix}- 8 x - 8 y = 120 \\ - 8 x + 8 y = \textcolor{w h i t e}{1} 24\end{matrix}\right.$
$\frac{\textcolor{w h i t e}{a a a a a a a a a a a a a a a}}{\textcolor{w h i t e}{a}}$

$- 8 x + \left(- 8 x\right) - \textcolor{red}{\cancel{\textcolor{b l a c k}{8 y}}} + \textcolor{red}{\cancel{\textcolor{b l a c k}{8 y}}} = 120 + 24$

$- 16 x = 144 \implies x = \frac{144}{- 16} = - 9$

Take this value of $x$ into the first equation and find the value of $y$

$- \left(- 9\right) - y = 15$

$- y = 15 - 9 \implies y = - 6$

Therefore, the two solutions to your system of equations are

$\left\{\begin{matrix}x = - 9 \\ y = - 6\end{matrix}\right.$