using computer to solve a system of nonlinear equations

Question

I was wondering if there is a program or website that solved a system of nonlinear equations I was trying a system that looks like this $$a+b = cd , a+c = bd ,a+d = bc$$ , ... it's like a pattern that share the idea of For all sets S⊆U such that $|S|=m$ and $|U|=2m $ , $$∏_{i∈S} qi = \sum_{i∈U∖S} qi $$

Answer 1

The system of equations $$a+b = cd , a+c = bd ,a+d = bc$$ has the solutions $(a,b,c,d)$ as follows: $$ (-b-1,b,-1,-1),\; (1-d,-1,-1,d),\; (1-c,-1,c,-1),\;(d(d-1),d,d,d). $$ This already shows a pattern.