Answer
The solution set is $\left\{ \left( -1,-1 \right) \right\}$.
Work Step by Step
By rewriting the first equation, we get:
$\begin{align}
& \frac{x}{6}-\frac{3y}{6}=\frac{2}{6} \\
& x-3y=2
\end{align}$
Therefore, the system can be rewritten as:
$\begin{align}
& x-3y=2 \\
& x+2y=-3
\end{align}$
And subtract the second equation from the first equation:
$\begin{align}
& x-3y-x-2y=2-\left( -3 \right) \\
& -5y=2+3 \\
& -5y=5 \\
& y=-1
\end{align}$
Substitute the value in the first equation and solve for x:
$\begin{align}
& x-3\left( -1 \right)=2 \\
& x+3=2 \\
& x=-1
\end{align}$.
Thus, The solution set is $\left\{ \left( -1,-1 \right) \right\}$.
