Augmented matrix format:
( 2 -3 1 | 2 )
( 1 1 1 | 8 )
( 3 -1 -1 | 0 )
R1⇔R2:
( 1 1 1 | 8 )
( 2 -3 1 | 2 )
( 3 -1 -1 | 0 )
R2-2R1 then R2*-1:
( 1 1 1 | 8 )
( 0 5 1 | 14 )
( 3 -1 -1 | 0 )
R3-3R1 then R3*(-1/4):
( 1 1 1 | 8 )
( 0 5 1 | 14 )
( 0 1 1 | 6 )
R2-R3 then R2/4:
( 1 1 1 | 8 )
( 0 1 0 | 2 )
( 0 1 1 | 6 )
R1-R3:
( 1 0 0 | 2 )
( 0 1 0 | 2 )
( 0 1 1 | 6 )
R3-R2:
( 1 0 0 | 2 )
( 0 1 0 | 2 )
( 0 0 1 | 4 )
(x,y,z)=(2,2,4)