2x+y+z=2 x+2y+z=4 x+y+2z=6

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2x+y+z=2x+2y+z=4x+y+2z=62x+y+z=2x+2y+z=4x+y+2z=62x+y+z=2x+2y+z=4x+y+2z=62x+y+z=2(1)x+2y+z=4(2)x+y+2z

2x+y+z=2 x+2y+z=4 x+y+2z=6
2x+y+z=2 x+2y+z=4 x+y+2z=6

2x+y+z=2 x+2y+z=4 x+y+2z=6
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

x=-1 y=1 z=3