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