Question: Question on simultaneous equation (potentially non-linear) solving: insufficient input

One can solve simultaneous equations if there are sufficient number of unique equations. If I do not have sufficient number of equations, I would like to generate a response that prints what is missing. How do I accomplish that? Any ideas? Thanks a lot in advance.

Trivial linear equation sample: 2x + 3y=0, y=2 - z. Solve x, y, z.

Given this problem, I should be able to print out something like "Not enough input to solve. Please input an equation involving x and z, or y and z, or x, or y, or z". The message should be an intelligent, calculated message, that is specific to the equations already provided. Otherwise, getting a message like "Please input a new unique equation involving x,y,z" is not very useful, since we all know that in order to solve equations of n variables n equations are sufficient.

Note that the solution should also work for non linear equations as well. The above example is linear, only to illustrate the problem definition.