To chip in two cents, and effectively summarising what has already been said:


1) You have two equations with n unknowns.

2) Therefore you can't uniquely determine all of the variables.

3) Therefore you need to solve for them to find if any solutions exist.

4) A basic way is to write nested loops and just iterate through all possibilities until you find an answer.

5) Clearly this is not a good solution; a better one is to write an optimization and minimise some objective function.

6) The time and computing power it will take to solve will depend on the number of variables you are trying to solve for. Solving for 10,000 variables is not going to be an easy task.


I'm afraid there isn't any way to avoid the facts.