Answer
$\{(3,-6)\}$
Work Step by Step
We are given the system of equations:
$\begin{cases}
5x-y=21\\
2x+3y=-12
\end{cases}$
Use the elimination method. Multiply the first equation by 3 and add it to the second equation to eliminate $y$ and determine $x$:
$\begin{cases}
3(5x-y)=3(21)\\
2x+3y=-12
\end{cases}$
$\begin{cases}
15x-3y=63\\
2x+3y=-12
\end{cases}$
$15x-3y+2x+3y=63-12$
$17x=51$
$x=3$
Determine $y$:
$5x-y=21$
$5(3)-y=21$
$15-y=21$
$y=15-21$
$y=-6$
The solution set of the system is:
$\{(3,-6)\}$
