Answer
$x=1$
$y=1$
$z=-2$
Work Step by Step
$ \begin{bmatrix}
10 & 10 & -20 & 60\\
15 & 20 & 30& -25\\
-5 & 30 & -10 & 45
\end{bmatrix} $
Divide all rows by -5.
$ \begin{bmatrix}
-2 & -2 & 4& -12\\
-3 & -4 & -6& 5\\
1 & -6 & 2 & -9
\end{bmatrix} $
Interchange the 1st and the 3rd row.
$ \begin{bmatrix}
1 & -6 & 2 & -9\\
-3 & -4 & -6& 5\\
-2 & -2 & 4& -12
\end{bmatrix} $
Add 3 times the 1st row to the 2nd row to produce a new 2nd row.
Add 2 times the 1st row to the 3rd row to produce a new 3rd row.
$ \begin{bmatrix}
1 & -6 & 2 & -9\\
0 & -22& 0& -22\\
0 & -14& 8& -30
\end{bmatrix} $
From the second row we can express $-22y=-22 \rightarrow y=1$
Use back-substitution to find the solution.
$y=1$
$-14y+8z=-30 \rightarrow z=-2$
$x-6y+2z=-9\rightarrow x=1$
