One algorithm for solving these is Gaussian elimination. If you're using Anarki (https://github.com/arclanguage/anarki), there's already a ready-made implementation in math.arc!
There's probably no way you could have known where to find this unless you asked, so thanks for the question. Please let us know if you have further questions about how to use this, or if you'd like to know more about any of these concepts.