Answer
$x=-2,y=5$
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:
$|D|=2(2)-(-1)(1)=5$
$|D_x|=-9(2)-(-1)8=-10$
$|D_y|=2(8)-(-9)(1)=25$
Thus
$x=\frac{|D_x|}{|D|}=-2,y=\frac{|D_y|}{|D|}=5,$