If Maxima was able to do so I guess that Mathcad and even Prime should be able to solve that system as well.
You may use the symbolic solve command or in Mathcad 15 you may even set up a solve block and evaluate it symbolically (not possible to do so in Prime).
Something like
This was done in Mathcad 15 and as you can see, the solve block gives you the solution in a column vector, while the symbolic solve gives you a row vector.