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