Answer
x = -4
y = -3
z = 6
Work Step by Step
Gaussian Elimination:
$\begin{bmatrix}
1 & 2 & -3 & |-28\\
0 & 4 & 2 & |0\\
-1 & 1 & -1 & |-5\\
\end{bmatrix}$ ~ $\begin{bmatrix}
1 & 2 & -3 & |-28\\
0 & 2 & 1 & |0\\
0 & 3 & -4 & |-33\\
\end{bmatrix}$ ~ $\begin{bmatrix}
1 & 2 & -3 & |-28\\
0 & 2 & 1 & |0\\
0 & 0 & -11 & |-66\\
\end{bmatrix}$
Back-Substitution:
Z:
-11z = -66
z = 6
Y:
2y + (1)6 = 0
2y = -6
y = -3
X:
x + 2(-3) - 3(6) = -28
x - 6 - 18 = -28
x - 24 = -28
x = -4
In Total:
x = -4
y = -3
z = 6
