Proving I can solve an equation without disclosing the solution (zero-knowledge proof)
For the discrete case, you can just use any zk-SNARK that generalizes over arithmetic circuits.
There is no direct way to do a zero-knowledge proof over the reals. However, you can map linear operations over real numbers to operations in the field you are working in by first proving an upper bound on your inputs. Since the circuit is public the verifier can independently check if the upper bound leads to overflow.