Question 902057
(0,3,-1)

3,3,1,8
2,-1,1,-4
1,2,1,5

divide row 1 by 3/1
1,1,1/3,8/3
2,-1,1,-4
1,2,1,5

add  down (-2/1) *row 1 to row 2
1,1,1/3,8/3
0,-3,1/3,-28/3
1,2,1,5

add  down (-1/1) *row 1 to row 3
1,1,1/3,8/3
0,-3,1/3,-28/3
0,1,2/3,7/3

divide row 2 by -3/1
1,1,1/3,8/3
0,1,1/-9,-28/-9
0,1,2/3,7/3

add  down (-1/1) *row 2 to row 3
1,1,1/3,8/3
0,1,1/-9,28/9
0,0,-21/-27,-21/27

divide row 3 by 7/9
1,1,1/3,8/3
0,1,1/-9,28/9
0,0,1,-1

We now have the value for the last variable.
We will work our way up and get the other solutions.

add up  (-1/-9) *row 3 to row 2
1,1,1/3,8/3
0,1,0,3
0,0,1,-1

add up  (-1/3) *row 3 to row 1
1,1,0,3
0,1,0,3
0,0,1,-1

add up  (-1/1) *row 2 to row 1
1,0,0,0
0,1,0,3
0,0,1,-1

final
1,0,0,0
0,1,0,3
0,0,1,-1
"0","3","-1"
(0,3,-1)