Question 918085
Adding (1) and (2) leads to
(x+y+z)+(x-z)=3+1
2x+y=4 
(4) y=4-2x 

Adding (1) and (3) leads to
(x+y+z)+(y-z)=3-4
x+2y=-1 

Replacing y with (4) leads to the solution for x:
x+2(4-2x)=-1
x+8-4x=-1
-3x=-9
x=3

Using x we can find y: 
y=4-2x=4-2(3)=4-6=-2
y=-2 

Next we find z:
x+y+z=3
3-2+z=3
-2+z=0
z=2 



solution: (3, -2, 2)