Question 119112
You didn't specify a solution method. 
Hopefully a matrix solution is OK.
[A][x]=[b]
where
[A]={{{(matrix(3,3,
3,-3, 3, 
2,2,3,
-3,2,2))
}}}
[x]={{{(matrix(3,1,
x,y,z))
}}}
[b]={{{(matrix(3,1,
-27,-3,-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]=(1/63)*{{{(matrix(3,3,
-2,12, -15, 
-13,15,-3,
10,3,12))
}}}
[Ainv][b]=(1/63)*{{{(matrix(3,3,
-2,12, -15, 
-13,15,-3,
10,3,12))
*(matrix(3,1,
-27,-3,-3))}}}
[x]={{{(matrix(3,1,
1,5,-5))
}}}
x=1
y=5
z=-5