Answer
$(-2,5)$
Work Step by Step
Step 1. Based on the Cramer’s Rule, we can define the determinants:
$\begin{array}( \\|D|= \\ \\ \end{array}
\begin{vmatrix} 2 &-1\\1 &2 \end{vmatrix},
\begin{array}( \\|D_x|= \\ \\ \end{array}
\begin{vmatrix} -9 &-1\\8 &2 \end{vmatrix},
\begin{array}( \\|D_y|= \\ \\ \end{array}
\begin{vmatrix} 2 &-9\\1&8 \end{vmatrix}$
Step 2. Evaluate the above determinants:
$|D|=2\times2-(-1\times1)=5$,
$|D_x|=-9\times2-(-1\times8)=-10$,
$|D_y|=2\times(-8)-(-9\times1)=25$
Step 3. Find the solutions as:
$x=\frac{|D_x|}{|D|}=-2$,
$y=\frac{|D_y|}{|D|}=5$
