# The Intersection of Two Implicit Functions in Maple

How would I find the intersection between the system of equations $2x^4-2y^3+y=0$ and $2x^2y+3y^4-2x=0$? The section in my book hasn't covered plot3d yet, so I was thinking perhaps implicitplot would be good, but I'm not sure if that's right command to use or not.If it is the right command, would the typical fsolve() method work on finding the points of intersection? Usually when I find solutions to a system of equations, I define the equations as functions,( say f and g) and then use fsolve(f(x)=g(x),x=-5..5) to find the solutions. But this isn't possible for an implicit function. How would I define something that isn't a function (such as a circle) in terms of a function in Maple? I change the last option accordingly to search for the solution, as I usually have the plot open in front of me. If anyone could offer any ideas, that would be appreciated.

• Note that the question is not just about where the two expressions (the left-hand-sides of the two equations) are equal to each other. The question is about where they are equal to each other AND (more importantly) where they are both individually equal to zero.
– acer
Oct 3, 2013 at 17:25

restart:

ee:=2*x^4-2*y^3+y=0;

ff:=2*x^2*y+3*y^4-2*x=0;

plots:-display(
plots:-implicitplot(ee,x=-4..4,y=-2..2, color=red),
plots:-implicitplot(ff,x=-4..4,y=-2..2, color=blue) );

sols:=solve({ee,ff}):
rsols := remove(hastype,evalf(map(op,{allvalues({sols})})),nonreal);

fsol1 := fsolve({ee,ff},{x=-4..4,y=-2..2});

seq( eval([ee,ff], s), s in rsols );