# How do you check your solutions to a systems of equations using the substitution method?

##### 1 Answer
Jan 26, 2015

I created a video with a more detail explanation here.

To check a system of equations by substitution, you plug your values for x and y into the original equations. If both simplified expressions are true then your answer is correct.

For example: To check if $\left(2 , - 3\right)$ was the correct solution for the system of equation: $y = - 2 x + 1$ and $y = x - 5$,
substitute 2 for x and -3 for y into each equation

$y = - 2 x + 1$
$- 3 = - 2 \left(2\right) + 1$
$- 3 = - 4 + 1$
$- 3 = - 3$

and

$y = x - 5$
$- 3 = 2 - 5$
$- 3 = - 3$

Since $x = 2$ and $y = - 3$ worked for both equations I know that $\left(2 , - 3\right)$ is the solution to this system of equations.