# Is the ordered pair (2,2) a solution to the system 2x - y = 2 and x + 3y =8?

May 10, 2016

Yes; $\left(x , y\right) = \left(2 , 2\right)$ is a solution to
$\textcolor{w h i t e}{\text{XXX}} 2 x - y = 2$ and
$\textcolor{w h i t e}{\text{XXX}} x + 3 y = 8$

#### Explanation:

Substituting $\left(\textcolor{red}{2} , \textcolor{b l u e}{2}\right)$ for $\left(\textcolor{red}{x} , \textcolor{b l u e}{y}\right)$

1. in the expression $2 \textcolor{red}{x} - \textcolor{b l u e}{y}$
gives $\left(2 \times \textcolor{red}{2}\right) + \textcolor{b l u e}{2} = 2$
So $\left(\textcolor{red}{2} , \textcolor{b l u e}{2}\right)$ is a solution for $2 \textcolor{red}{x} - \textcolor{b l u e}{y} = 2$
2. in the expression $\textcolor{red}{x} + 3 \textcolor{b l u e}{x}$
gives $\textcolor{red}{2} + \left(3 \times \textcolor{b l u e}{2}\right) = 8$
So $\left(\textcolor{red}{2} , \textcolor{b l u e}{2}\right)$ is a solution for $\textcolor{red}{x} + 3 \textcolor{b l u e}{y} = 8$

Since $\left(\textcolor{red}{2} , \textcolor{b l u e}{2}\right)$ is a solution for both equations,
it is a solution for the system of equations (since the system is comprised of only those two equations).