This is a class of problems known as constraint solvers, and a program like Solvespace is actually using a symbolic algebra system under the hood to 'solve' the

This is a class of problems known as constraint solvers, and a program like Solvespace is actually using a symbolic algebra system under the hood to 'solve' the layout as you constraint the sketch in the GUI in nearly the exact way that SymPy is solving the puzzle above. There are various approaches; Solvespace uses a modified Newton's method and was written in C++ making use of just the Eigen lib.