Answer
Solution set = $\{(3,-1)\}$
Work Step by Step
$D= $determinant of the coefficient matrix
$=\left|\begin{array}{ll}
4 & -5\\
2 & 3
\end{array}\right|=4(3)-(-5)(2)=22$
$D_{x}=$ in D, replace the x column with the constants column
$=\left|\begin{array}{ll}
17 & -5\\
3 & 3
\end{array}\right|=51+15=66$
$D_{y}=$ in D, replace the x column with the constants column
$=\left|\begin{array}{ll}
4 & 17\\
2 & 3
\end{array}\right|=12-34=-22$
$x=\displaystyle \frac{D_{x}}{D}=\frac{66}{22}=3$
$y=\displaystyle \frac{D_{y}}{D}=\frac{-22}{22}=-1$
Solution set = $\{(3,-1)\}$