Question 635926
The inverse of variables is turning you up side down! Fix it!
Merely let a = 1/x, b = 1/y and c = 1/z and yield the friendly 3x3 system of equations
           2a +  3b - 2c = -1
           3a - 18b + 5c =  4
           5a +  3b -  c =  1
Use Mathcad or your handy dandy TI-84 to get a, b and c. Then just get their inverse to get x, y, and z. You can also solve "by hand" using the inverse of a 3x3 matrix.