TITLE: Solution of system of non-linear equations
QUESTION [7 upvotes]: Is there a general condition for the existence and uniqueness of solution of a system of simultaneous non-linear equations similar to the determinant test for a system of linear equations.
What are the solution methods (theoretical and numerical) for solving a system of simultaneous non-linear equations.

REPLY [4 votes]: @Julie Kirk;
Iteration is the main weapon to solve them. Newton's is just one iterative method. If you ever want to get into some of the practical problems connected with getting good initial guesses and then solving try "Numerical Methods that Work (Usually)" by Forman S. Acton or "Real Computing Made Real" by Acton. But only if you are serious about knowing because they are difficult.