You can
put this solution on YOUR website! Since algebra.com doesn't do matrices very well, I will just show the rectangular array of numbers.
x+y+z=9
3x-y+z=-1
-2x+2y-3z=-2
translates into the augmented matrix:
1 1 1 9
3 -1 1 -1
-2 2 -3 -2
Added -3 times row 1 to row 2.
1 1 1 9
0 -4 -2 -28
-2 2 -3 -2
Added 2 times row 1 to row 3.
1 1 1 9
0 -4 -2 -28
0 4 -1 16
Replaced row 2 with -1/4 times row 2.
1 1 1 9
0 1 1/2 7
0 4 -1 16
Added -1 times row 2 to row 1.
1 0 1/2 2
0 1 1/2 7
0 4 -1 16
Added -4 times row 2 to row 3.
1 0 1/2 2
0 1 1/2 7
0 0 -3 -12
Replaced row 3 with -1/3 times row 3.
1 0 1/2 2
0 1 1/2 7
0 0 1 4
Added -1/2 times row 3 to row 1.
1 0 0 0
0 1 1/2 7
0 0 1 4
Added -1/2 times row 3 to row 2.
1 0 0 0
0 1 0 5
0 0 1 4
which translates back into:
x = 0
y = 5
z = 4
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