Question 121386
x+y+z=5
x-y+z=1
x-y-z=3


You didn't specify a solution method. 
Hopefully a matrix solution is OK.
[A][x]=[b]
where
[A]={{{(matrix(3,3,
1,1,1,
1,-1,1,
1,-1,-1))}}}
[x]={{{(matrix(3,1,x,y,z))}}}
[b]={{{(matrix(3,1,5,1,3))}}}
We then need to find the inverse of [A]([Ainv]) and matrix multiply by [b] to get [x].
[A][x]=[b]
[x]=[Ainv][b]
[Ainv]={{{(1/4)*(matrix(3,3,
2,0,2,
2,-2,0,
0,2,-2))}}}
[Ainv][b]={{{(1/4)*(matrix(3,3,
2,0,2,
2,-2,0,
0,2,-2))*(matrix(3,1,5,1,3))}}}
[x]={{{(matrix(3,1,4,2,-1))}}}
x=4
y=2
z=-1