Answer
Solution set = $\displaystyle \{(-1,\dfrac{5}{2})\}$
Work Step by Step
$D= $determinant of the coefficient matrix
$=\left|\begin{array}{ll}
3 & 2\\
2 & 2
\end{array}\right|=3(2)-(2)(2)=2$
$D_{x}=$ in D, replace the x column with the constants column
$=\left|\begin{array}{ll}
2 & 2\\
3 & 2
\end{array}\right|=4-6=-2$
$D_{y}=$ in D, replace the x column with the constants column
$=\left|\begin{array}{ll}
3 & 2\\
2 & 3
\end{array}\right|=9-4=5$
$x=\displaystyle \frac{D_{x}}{D}=\frac{-2}{2}=-1$
$y=\displaystyle \frac{D_{y}}{D}=\frac{5}{2}$
Solution set = $\displaystyle \{(-1,\frac{5}{2})\}$
