Answer
$x=-3$
$y=2$
$z=1$
Work Step by Step
First we have to compute the determinants $D,D_x,D_y,D_z$:
$D=\begin{vmatrix}2&1&0\\0&1&-2\\3&0&-2\end{vmatrix}=-4-6+0-0-0-0=-10$
$D_x=\begin{vmatrix}2&1&0\\0&1&-2\\3&0&-2\end{vmatrix}=8+22+0-0-0-0+30$
$D_y=\begin{vmatrix}2&1&0\\-4&0&-11\\3&0&-2\end{vmatrix}=0+24+0-0-44-0=-20$
$D_z=\begin{vmatrix}2&1&0\\0&1&-2\\-4&0&-11\end{vmatrix}=-22+0+0+12-0-0=-10$
We use Cramer's Rule to determine the solutions of the system:
$x=\dfrac{D_x}{D}=\dfrac{30}{-10}=-3$
$y=\dfrac{D_y}{D}=\dfrac{-20}{-10}=2$
$z=\dfrac{D_z}{D}=\dfrac{-10}{-10}=1$
The solution is:
$x=-3$
$y=2$
$z=1$
