Answer
$(-2, 6)$
Work Step by Step
Step 1. Based on the Cramer’s Rule, with the given equations, we can define the following determinants:
$\begin{array}( \\|D|= \\ \\ \end{array}
\begin{vmatrix} 1/2 &1/3\\1/4 &-1/6 \end{vmatrix},
\begin{array}( \\|D_x|= \\ \\ \end{array}
\begin{vmatrix} 1 &1/3\\-3/2 &-1/6 \end{vmatrix},
\begin{array}( \\|D_y|= \\ \\ \end{array}
\begin{vmatrix} 1/2 &1\\1/4 &-3/2 \end{vmatrix}$
Step 2. Evaluate the above determinants:
$|D|=-\frac{1}{12}-\frac{1}{12}=-\frac{1}{6}$,
$|D_x|=-\frac{1}{6}+\frac{1}{2}=\frac{1}{3}$,
$|D_y|=-\frac{3}{4}-\frac{1}{4}=-1$
Step 3. Find the solutions as:
$x=\frac{|D_x|}{|D|}=-2$,
$y=\frac{|D_y|}{|D|}=6$
