Automatic Math Equation Solver?

I’m working on a computer science project and I have quite a few simple equations to solve. Is there a program (Linux or Windows, preferably free) that would solve the following for me?

20y + a = (3 + b)x
(3+c)y + x = 25

where I want to know all the integer values of x, y, a, b, and c, given a, b and c could be arbitrary integers with which I could provide some limits (e.g. a >= 0).

That’s just an example problem. It takes quite a bit of time to get a possible set of solutions for each of these and this project isn’t really about math.

Does anybody know of one?

Thanks