Answer
Solution set = $\{(2,-3)\}$
Work Step by Step
$D= $determinant of the coefficient matrix
$=\left|\begin{array}{ll}
12 & 3\\
2 & -3
\end{array}\right|=-36-6=-42$
$D_{x}=$ in D, replace the x column with the constants column
$= \left|\begin{array}{ll}
15 & 3\\
13 & -3
\end{array}\right|=-45-39=-84$
$D_{y}=$ in D, replace the x column with the constants column
$=\left|\begin{array}{ll}
12 & 15\\
2 & 13
\end{array}\right|=156-30=126$
$x=\displaystyle \frac{D_{x}}{D}=\frac{-84}{-42}=2$
$y=\displaystyle \frac{D_{y}}{D}=\frac{126}{-42}=-3$
Solution set = $\{(2,-3)\}$