Algorithm for solving system of nonlinear equations

[mooshasta]

I'm trying to find an algorithm to solve a 4 variable system of nonlinear equations.. the variables are named w,x,y,z and a,b,c,d are constants:

a = x - y + z
b = w + x
c = y * z
d = x * y / w


Can anyone offer any advice? Much appreciated...

 

[Hurkyl]

Gröbner basis algorithms could be used to, for example, eliminate all but one variable.