Question 1146813
This was done without rechecking:

<pre>
2  1  -1  -1
3  -3  -1 5
1 -2  3   6

0  5  -8  -13
0  3  -10 -13
1 -2  3   6
then switch rows

1  -2  3  6
0  5  -8 -13
0  3  -10 -13

1  -2  3  6
0  15 -24 -29
0  15 -50 -65

E3-E3-E2;
E2+8E3 and  E1-3E3

1 -2 0 3
0  5 0 -5
0  0 1  1

1 -2  0  3
0  1  0 -1
0 0  1  1

then E1=E1+2E2

1  0  0  1
0  1  0 -1
0  0  1  1

</pre>
{{{system(x=1,y=-1,z=1)}}}