Answer
$\{(-3,6)\}$
Work Step by Step
Use Cramer's rule, we have:
1. $D=\begin{vmatrix} 5 & 2 \\ 4 & -3 \end{vmatrix}=(5)(-3)-(2)(4)=-23$
2. $D_x=\begin{vmatrix} -3 & 2 \\ -30 & -3 \end{vmatrix}=(-3)(-3)-(2)(-30)=69$
3. $D_y=\begin{vmatrix} 5 & -3 \\ 4 & -30 \end{vmatrix}=(5)(-30)-(-3)(4)=-138$
4. $x=\frac{D_x}{D}=\frac{69}{-23}=-3$ and $y=\frac{D_y}{D}=\frac{-138}{-23}=6$
5. Thus the solution set is $\{(-3,6)\}$
