Answer is: x such that #x=-z-2#, y=1, and z such that #z=-x-2#
Explanation:
Add equation 1 to equation 3 to get: #3y=3#, So #y=1#. Plugging this in to the other equations, you get some form of #x+z=-2# (equation 1). Equation 2 becomes #2x+2z=-4# and Equation 3 becomes #-x-z=2#.