Answer
$x=23$
$y=-12$
$z=3$
Work Step by Step
First we have to compute the determinants $D,D_x,D_y,D_z$:
$D=\begin{vmatrix}1&2&2\\2&4&7\\-2&-5&-2\end{vmatrix}=-8-28-20+16+35+8=3$
$D_x=\begin{vmatrix}5&2&2\\19&4&7\\8&-5&-2\end{vmatrix}=-40+12-190-64+175+76=69$
$D_y=\begin{vmatrix}1&5&2\\2&19&7\\-2&8&-2\end{vmatrix}=-38-70+32+76-56+20=-36$
$D_z=\begin{vmatrix}1&2&5\\2&4&19\\-2&-5&8\end{vmatrix}=32-76-50+40+95-32=9$
We use Cramer's Rule to determine the solutions of the system:
$x=\dfrac{D_x}{D}=\dfrac{69}{3}=23$
$y=\dfrac{D_y}{D}=\dfrac{-36}{3}=-12$
$z=\dfrac{D_z}{D}=\dfrac{9}{3}=3$
The solution is:
$x=23$
$y=-12$
$z=3$
