y+2z=-2 (1)
3x+y-4z=1 (2)
2x-y+2z=8 (3)
(1)+(3)
2x+4z=6
x+2z=3 (4)
(2)+(3)
5x-2z=9 (5)
(4)+(5)
6x=12
x=2
z=(3-x)/2=1/2
y=2x+2z-8=-3