# Is the ordered pair (2,3) a solution of the system of linear equations -2x+3y=5 and 3x+2y=12?

Apr 26, 2016

Yes

#### Explanation:

Substituting $\left(\textcolor{red}{2} , \textcolor{b l u e}{3}\right)$ for $\left(\textcolor{red}{x} , \textcolor{b l u e}{y}\right)$

• in $- 2 \textcolor{red}{x} + 3 \textcolor{b l u e}{y}$
$\textcolor{w h i t e}{\text{XXX}}$gives $- 2 \left(\textcolor{red}{2}\right) + 3 \left(\textcolor{b l u e}{3}\right) = - 4 + 9 = 5$
$\textcolor{w h i t e}{\text{XXX}}$So the given coordinates are a solution to the first equation.
• in $3 \textcolor{red}{x} + 2 \textcolor{y}{=} 12$
$\textcolor{w h i t e}{\text{XXX}}$gives $3 \left(\textcolor{red}{2}\right) + 2 \left(\textcolor{b l u e}{3}\right) = 6 + 6 = 12$
$\textcolor{w h i t e}{\text{XXX}}$So the given coordinates are a solution to the second equation.

Since the given coordinates are a solution to both equations,
they are a solution to the system of equations.