Given n equations in n unknowns:

a*f(x) + b*g(y) = c

d*f(x) + e*g(y) = f

If there is a solution to these equations, you can use substitution to transform these equations into a set of linear equations and solve using linear algebra.

Let f(x) = u and g(y) = v

Then

a*f(x) + b*g(y) = c

d*f(x) + e*g(y) = f

which becomes

a*u + b*v = c

d*u + e*v = f

Which can be solved for u and v using linear algebra.

x and y can then be solved for by solving the corresponding equations

u = f(x), and v = g(y) thus making it possible to solve systems of non-linear equations of the form above using linear algebra.

Any thoughts?

Edwin G. Schasteen