I was wondering if I could get some references for my problem.
I have three highly non-linear equations:
$$f_{1}(x,y,z) = 0$$
$$f_{2}(x,y,z) = 0$$
$$f_{3}(x,y,z) = 0$$
I want to see if the variable $z$ is not redundant. For instance, after rearranging the three equations, if I'm in a situation where
$$\tilde{f}_{1}(x,y) = 0$$
$$\tilde{f}_{2}(x,y) = 0$$
$$x+y+z = 0$$
then, $z$ naturally follows from $(x^{*},y^{*})$ that solves the first two equations.
What would be the steps to examine this issue numerically? I thought this was related to the rank problem, but I couldn't find more. Any suggestions would be very much appreciated.
Maybe I was unclear about what I meant by "redundant". I wanted to say a variable that can be directly inferred from the other variables.