(1) Maybe the following problem is closely related to "An easily corrected limitation to symbolic derivatives in fsolve() when solving a system of equations" in TomM's blog.

(2) The problem: I would like to solve a set of equations with

     fsolve({f(x,y)=0,g(x,y)=0},{x,y},{x=-10..10,y=-10..10};

      with the procedures