2x+y=11

multiply by 2

4x+2y=22

z+2y=12

------

4x-z=10

------

z+2x=8

multiply by 2

4x+2z=16

4x-z=10

------

-3z=-6

z=2

x=3

y=5

so,,,

2x+3y+4z=29

multiply by 2

4x+2y=22

z+2y=12

------

4x-z=10

------

z+2x=8

multiply by 2

4x+2z=16

4x-z=10

------

-3z=-6

z=2

x=3

y=5

so,,,

2x+3y+4z=29