Answer
x = 5
y = -1
z = -2
Work Step by Step
Gaussian Elimination:
$\begin{bmatrix}
3 & -2 & 1 & |15\\
-1 & 1 & 2 & |-10\\
1 & -1 & -4 & |14\\
\end{bmatrix}$ ~ $\begin{bmatrix}
1 & -1 & -4 & |14\\
-1 & 1 & 2 & |-10\\
3 & -2 & 1 & |15\\
\end{bmatrix}$ ~ $\begin{bmatrix}
1 & -1 & -4 & |14\\
0 & 0 & -2 & |4\\
0 & 1 & 13 & |-27\\
\end{bmatrix}$ ~ $\begin{bmatrix}
1 & -1 & -4 & |14\\
0 & 1 & 13 & |-27\\
0 & 0 & -2 & |4\\
\end{bmatrix}$
Back-Substitution:
Z:
-2z = 4
z = -2
Y:
y + (-2)(13) = -27
y - 26 = -27
y = -1
X:
x - (1)(-1) - 4(-2) = 14
x + 1 + 8 = 14
x + 9 = 14
x = 5
In Total:
x = 5
y = -1
z = -2
