Answer
$(5, -5, -4)$
Work Step by Step
Step 1. Define the following determinants:
$|D|=\begin{vmatrix} 2&0&-1\\3&-1&5\\4&2&3\end{vmatrix},
|D_x|=\begin{vmatrix} 14&0&-1\\0&-1&5\\-2&2&3\end{vmatrix},
|D_y|=\begin{vmatrix} 2&14&-1\\3&0&5\\4&-2&3\end{vmatrix},
|D_z|=\begin{vmatrix} 2&0&14\\3&-1&0\\4&2&-2\end{vmatrix} $
Step 2. Evaluate the determinants (use row1 expansions, row3 expansion for $|D_y|$):
$|D|=2(-3-10)-1(6+4)=-36, |D_x|=14(-3-10)-1(0-2)=-180, |D_y|=-3(42-2)-5(-4-56)=180, |D_z|=2(2-0)+14(6+4)=144$
Step 3. Find solution to the system using Cramer's Rule:
$x=\frac{|D_x|}{|D|}=5, y=\frac{|D_y|}{|D|}=-5, z=\frac{|D_z|}{|D|}=-4$ which gives $(5, -5, -4)$
