Level curves to two functions for solving nonlinear system of equations.

I want to solve a system of nonlinear equations:

x^2 + y*sin(y) - 3 = 0 x*y + exp(x) + y -5 = 0

So I introduced the two functions f1 = x^2 + y*sin(y) - 3 and f2 = x*y + exp(x) + y -5. Now I am trying to plot the level curves(at 0) so I can see how many solutions exists. But I am unable to plot a meaningful result(i.e finding the intersections).

if true
  % %%
x=linspace(-15,15,400); 
y=linspace(-15,15,400);
f=@(x,y)(x.^2+y.*sin(y)-3);
[X,Y]=meshgrid(x,y);
Z=f(X,Y);
contour(X,Y,Z,10)
hold on
f=@(x,y)(x*y+exp(x)+y-5);
[X,Y]=meshgrid(x,y);
Z=f(X,Y);
contour(X,Y,Z,100)
end

[John D'Errico]

Why do you need the (if true)?

Answer 1

[John D'Errico]

It looks like you are almost there.

Use contourc to get the contours as a set of polygons. Then use a tool from the file exchange to generate the intersections between the polygons. Doug's curve intersections tool is the one I'd choose.

In the event that there are several broken polygons produced by contourc, you will need to be careful to ensure you find all the intersections.