Answer
$x=5,$
$y=0,$
$z=1$
Work Step by Step
$\begin{cases}
x-4z=1\\
2x-y-6z=4\\
2x+3y-2z=8
\end{cases}$
Multiplying Equation 2 by -1 and adding it to Equation 3, results in new Equation 3.
$\begin{cases}
-2x+y+6z=-4\\
2x+3y-2z=8\\
-- -- -- -- \\
4y+4z=4
\end{cases}$
Multiplying Equation 1 by -2 and adding it to Equation 2, results in new Equation 2.
$\begin{cases}
-2x+8z=-2\\
2x-y-6z=4\\
-- -- -- -- --\\
-y+2z=2
\end{cases}$
Multiplying new Equation 2 by 4 and adding it to new Equation 3.
$\begin{cases}
4y+4z=4\\
-4y+8z=8\\
-- -- --\\
12z=12
\end{cases}$
Thus, $z=1$. Substituting back into Equation 1, $x-4=1, x=5$.
Substituting back into Equation 2, $10-y-6=4, y=0$
