Answer
$(-5,-2,7)$
Work Step by Step
Formula to determine the determinant, $D$ of a $3 \times 3$ matrix is:
$D=\begin{vmatrix}a&b&c\\d&e&f\\g&h&i\end{vmatrix}=a \begin{vmatrix}e&f\\h&i\end{vmatrix}-b \begin{vmatrix}d&f\\g&i\end{vmatrix}+c \begin{vmatrix}d&e\\g&h\end{vmatrix}$
Need to apply Cramer's Rule.
$x=\dfrac{D_x}{D};y=\dfrac{D_y}{D}; z=\dfrac{D_z}{D}$
Now
$D=\begin{vmatrix}1&1&1\\2&-1&1\\-1&3&-1\end{vmatrix}=4$;
$D_x=\begin{vmatrix}0&1&1\\-1&-1&1\\-8&3&-1\end{vmatrix}=-20$;
$D_y=\begin{vmatrix}1&0&1\\2&-1&1\\-1&-8&-1\end{vmatrix}=-8$
$D_z=\begin{vmatrix}1&1&0\\2&-1&-1\\-1&3&-8\end{vmatrix}=28$
Thus,
$x=\dfrac{-20}{4}=-5;y=\dfrac{-8}{4}=-2; z=\dfrac{28}{4}=7$
Hence, $(x,y,z)=(-5,-2,7)$
