Answer
$x=-5$
$y=-2$
$z=7$
Work Step by Step
First we have to compute the determinants $D,D_x,D_y,D_z$:
$D=\begin{vmatrix}1&1&1\\2&-1&1\\-1&3&-1\end{vmatrix}=1(1-3)-1(-2+1)+1(6-1)=4$
$D_x=\begin{vmatrix}0&1&1\\-1&-1&1\\-8&3&-1\end{vmatrix}=0(1-3)-1(1+8)+1(-3-8)=-20$
$D_y=\begin{vmatrix}1&0&1\\2&-1&1\\-1&-8&-1\end{vmatrix}=1(1+8)-0(-2+1)+1(-16-1)=-8$
$D_z=\begin{vmatrix}1&1&0\\2&-1&-1\\-1&3&-8\end{vmatrix}=1(8+3)-1(-16-1)+0(6-1)=28$
We use Cramer's Rule to determine the solutions of the system:
$x=\dfrac{D_x}{D}=\dfrac{-20}{4}=-5$
$y=\dfrac{D_y}{D}=\dfrac{-8}{4}=-2$
$z=\dfrac{D_z}{D}=\dfrac{28}{4}=7$
The solution is:
$x=-5$
$y=-2$
$z=7$
