Using fsolve() to solve non-linear system equation

[parisse]

For univariate equations, a sign change on an interval warrants a root for a continuous fonction, it's not hard to implement a numeric solver on an interval. There is unfortunately no easy generalization for multivariate fonctions. That's why there is only an iterative implementation for generic systems, requiring a initial guess. However, polynomial systems like your system can be solved without initial guess with solve or fsolve (with [x,y] as 2nd argument).