Question 899754
2,2,1,-7
1,0,1,-3
0,4,-3,13

divide row 1 by 2
1,1,1/2,-7/2
1,0,1,-3
0,4,-3,13

add  down (-1) *row 1 to row 2
1,1,1/2,-7/2
0,-1,1/2,1/2
0,4,-3,13

add  down (0) *row 1 to row 3
1,1,1/2,-7/2
0,-1,1/2,1/2
0,4,-3,13

divide row 2 by -1
1,1,1/2,-7/2
0,1,1/-2,1/-2
0,4,-3,13

add  down (-4) *row 2 to row 3
1,1,1/2,-7/2
0,1,1/-2,1/-2
0,0,-1,15

divide row 3 by -1
1,1,1/2,-7/2
0,1,1/-2,1/-2
0,0,1,-15

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

add up  (1/2) *row 3 to row 2
1,1,1/2,-7/2
0,1,0,-8
0,0,1,-15

add up  (-1/2) *row 3 to row 1
1,1,0,4
0,1,0,-8
0,0,1,-15

add up  (-1) *row 2 to row 1
1,0,0,12
0,1,0,-8
0,0,1,-15


"12","-8","-15"
(12,-8,-15)