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