I'd suggest to use ParametricPlot3D (see attachement). The Student and full version of Mathematica are usually the same in function. I've the home edition of Mathematica 9 on my private laptop and it's absolutely identical with the full version on our institute's computers.
In Mathematica, any version, Plot3D wants an expression or function giving z values as a function of x and y coordinates so... turn x+z==0 into x==-z into -(x+0*y)==z (or just plot -x) and now you have a function giving z values to plot.
Carefully check some points on the surface to verify this is correct.
And, if you don't already know... this ---> (*==z*) <--- is a comment in Mathematica code.