Answer
$x=-1, y =2 \text{ or } (-1, 2)$
Work Step by Step
The system of equations is given by the following two equations:
$$\begin{cases}
x+3y=5 \hspace{20pt} (1)\\[3mm]
2x-3y=-8 \hspace{20pt} (2)
\end{cases}$$
$\text{The coefficients of y in the two equations are additive inverses.}$
$\text{Therefore, we add the two equations to eliminate y"}$
\[
\begin{aligned} &x+3y=5 \\[2mm]
&2x-3y=-8 \\[3mm]
\hline & 3x=-3 \\[2mm]
&x =-1
\end{aligned}
\]
$\text{Substituting in equation (1) for } x=-1$ gives:
$$-1+3y=5\\[3mm]3y=5+1 \\[3mm] 3y=6 \\[3mm] y=2$$
Therefore, the solution is:
$\boxed{x=-1 \hspace{20pt} y =2}$
