# Checking a System of Equations

How to check your answer to a system of equations, using substitution

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Another example:

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 $(2, -3)$ was the correct solution for the system of equation:

$y = -2x + 1$ and $y = x – 5$,

substitute $2$ for$x$ and $-3$ for $y$ into each equation

\begin{align*} y &= 2x + 1 \\ -3 &=-2(2) + 1 \\ -3 &= -4 + 1 \\ -3 &= -3 \end{align*}
and
\begin{align*} y &= x – 5 \\ -3 &=2 – 5 \\ -3 &= -3 \end{align*}