Answer
$y=6,x=2$
Work Step by Step
We know that for a matrix \[ \left[\begin{array}{rr} a & b \\ c &d \\ \end{array} \right] \] the determinant, $D=ad-bc.$
Thus the determinant of the coefficient matrix: $D=2\cdot2-(-1)\cdot1=4+1=5.$
Then applying Cramer's Rule: $y=\frac{\begin{vmatrix} 2 & -2\\ 1 & 14 \\ \end{vmatrix}}{5}=\frac{2\cdot14-(-2)\cdot1}{5}=\frac{30}{5}=6$
$x=\frac{\begin{vmatrix} -2 & -1 \\ 14 & 2 \\ \end{vmatrix}}{5}=\frac{-2\cdot2-(-1)\cdot14}{5}=\frac{10}{5}=2$ Thus $y=6,x=2$
