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