2 -1 3 4
3 2 1 -1
-1 3 2 5
1 -0.5 1.5 2 0.5*R1
3 2 1 -1
-1 3 2 5
1 -0.5 1.5 2
0 3.5 -3.5 -7 R2 - 3*R1
-1 3 2 5
1 -0.5 1.5 2
0 3.5 -3.5 -7
0 2.5 3.5 7 R3 + R1
1 -0.5 1.5 2
0 1 -1 -2 0.285714*R2
0 2.5 3.5 7
1 -0.5 1.5 2
0 1 -1 -2
0 0 6 12 R3 - 2.5*R2
1 -0.5 1.5 2
0 1 -1 -2
0 0 1 2 (1/6)*R3
The Matrix is now in reduced echelon form (ref) and it is upper triangular
1 -0.5 1.5 2
0 1 0 0 R2 + R3
0 0 1 2
1 -0.5 0 -1 R1 - 1.5*R3
0 1 0 0
0 0 1 2
1 0 0 -1 R1 + 0.5*R2
0 1 0 0
0 0 1 2
The Matrix is now in reduced row echelon form (rref)
So the answers are x = -1, y = 0 and z = 2
The answer as an ordered triple is (-1, 0, 2)