Solve system of polynomial equations

Question

I have a system consisting of 2 polynomials, in 2 variables, with complex coefficients. The general case consists of a finite number of pairs of complex numbers.

NSolve[{poly1==0,poly2==0},{x,y}]

in Mathematica works for lower degree polynomials, but the time needed to find all roots seems to be exponential, 2^deg. Is there an alternative to NSolve, which is more efficient? In other language? The degree we're aiming for is in the range 15-25, higher is better.

Answer 1

I did not find a solution, but seems like lesser number of cores is better. (Compared with 2,4 and 50 processor cores), and 64 bit architecture is 2 times faster.

All this using NSolve. System of 2 degree 17 polynomials in 2 variables took 24 hours to solve.