# Is (-5, -1) a solution to this system of equations 3y = -2x - 13  and -4x = -8y+12?

Feb 25, 2017

Because $\left(- 5 , - 1\right)$ is a solution for both equations it is also a solution for the system of those two equations.

#### Explanation:

First, substitute $\textcolor{red}{- 5} \mathmr{and}$color(blue)(-1)$f \mathmr{and}$color(red)(x) and $\textcolor{b l u e}{y}$ in the first equation and see if both sides of the equation calculate to the same value:

$3 \textcolor{b l u e}{y} = - 2 \textcolor{red}{x} - 13$ becomes:

$3 \times \textcolor{b l u e}{- 1} = \left(- 2 \times \textcolor{red}{- 5}\right) - 13$

$- 3 = 10 - 13$

$- 3 = - 3$

The first, equation has $\left(- 5 , - 1\right)$ as a solution. Now, substitute $\textcolor{red}{- 5} \mathmr{and}$color(blue)(-1)$f \mathmr{and}$color(red)(x) and $\textcolor{b l u e}{y}$ in the second equation and see if both sides of the equation calculate to the same value:

$- 4 \textcolor{red}{x} = - 8 \textcolor{b l u e}{y} + 12$ becomes:

$- 4 \times \textcolor{red}{- 5} = \left(- 8 \times \textcolor{b l u e}{- 1}\right) + 12$

$20 = 8 + 12$

$20 = 20$