# How do you solve -13x-17y=15 and x+y=-3?

Feb 19, 2017

$x = - 9$ and $y = 6$

#### Explanation:

$- 13 x - 17 y = 15$
$x + y = - 3$

From the second equation, determine a value for $x$.

$x + y = - 3$

Subtract $y$ from each side.

$x = - 3 - y$

In the first equation, substitute $x$ with $\textcolor{red}{\left(- 3 - y\right)}$.

$- 13 x - 17 y = 15$

$- 13 \textcolor{red}{\left(- 3 - y\right)} - 17 y = 15$

Open the brackets and simplify. The product of two negatives is a positive.

$39 + 13 y - 17 y = 15$

$39 - 4 y = 15$

Subtract $39$ from both sides.

$- 4 y = - 24$

Divide both sides by $- 4$.

$y = 6$

in the second equation, substitute $y$ with $\textcolor{b l u e}{6}$.

$x + y = - 3$

$x + \textcolor{b l u e}{6} = - 3$

Subtract $6$ from both sides.

$x = - 9$