Answer
Solution set = $\{(4,2)\}$
Work Step by Step
$D= $determinant of the coefficient matrix
$=\left|\begin{array}{ll}
3 & -4\\
2 & 2
\end{array}\right|=3(2)-(-4)(2)=14$
$D_{x}=$ in D, replace the x column with the constants column
$=\left|\begin{array}{ll}
4 & -4\\
12 & 2
\end{array}\right|=8+48=56$
$D_{y}=$ in D, replace the x column with the constants column
$=\left|\begin{array}{ll}
3 & 4\\
2 & 12
\end{array}\right|=36-8=24$
$x=\displaystyle \frac{D_{x}}{D}=\frac{56}{14}=4$
$y=\displaystyle \frac{D_{y}}{D}=\frac{28}{14}=2$
Solution set = $\{(4,2)\}$
