There are powerful tools out there that can do this type of computation and more in a breeze. I have personally worked on SaturnAPI [0], which is a RESTful API for Matlab/Octave. You can build your own APIs to do almost any calculation imaginable. If anyone needs to solve equations, definitely give it a shot. You can solve all sorts of equations, linear and non-linear [1].

[0] https://saturnapi.com/

[1] http://www.mathworks.com/help/symbolic/equation-solving.html