Answer
$x=3 , y =-6 \text{ or } (3, -6)$
Work Step by Step
The system of equations is given by the following two equations:
$$\begin{cases}
5x-y=21 \hspace{20pt} (1)\\[3mm]
2x+3y=-12 \hspace{20pt} (2)
\end{cases}$$
$\text{Multiply equation (1) by 3 so that the coefficients of y in the two equations are additive inverses.}$
$15x-3y=63\hspace{20pt} (1)$
$\text{Therefore, we add the two equations to eliminate y:}$
\[
\begin{aligned} &15x-3y=63\\[2mm]
&2x+3y=-12 \\[3mm]
\hline & 17x=51 \\[2mm]
&x =3
\end{aligned}
\]
$\text{Substituting in equation (1) for } x=3$ gives:
$$5(3)-y=21\\[3mm]15-y=21 \\[3mm] y=15-21 \\[3mm] y=-6$$
Therefore, the solution is:
$\boxed{x=3 \hspace{20pt} y =-6}$
