Answer
$x=-2,y=6$
Work Step by Step
Cramer's Rule for $2$ equations in $2$ unknowns says that the system of linear equations is equivalent to the matrix equation $DX=B$ and if $|D|\ne 0$, then the solutions are $x_i=\frac{|D_{x_i}|}{|D|}$ where $D_{x_i}$ can be obtained by replacing the $i$th column of $D$ by $B$
Hence, we have:
$|D|=0.5(-1/6)-(1/3)(1/4)=-1/6$
$|D_x|=1(-1/6)-(1/3)(-3/2)=1/3$
$|D_y|=0.5(-3/2)-(1)(1/4)=-1$
Thus
$x=\frac{|D_x|}{|D|}=-2,y=\frac{|D_y|}{|D|}=6$
