system of equations - (difficult problem)

How does one solve the system of equations:

x = 3y - 4y^3

y = 3x - 4x^3

The problem statement is pretty simple but by using conventional method of replacing variables I get a 9th degree equation in y or x - depending which variable you replace - (impossible to solve normally).

The best I can do is bring that 9th degree equation down to a 6th degree equation (which is still impossible to solve).

Anybody have any pointers for me to proceed in the right direction?

Thanks a lot.