Re: System of equations
These are either olympiad problems, in which case there is a general method which I do not know yet. Solving numerically I can do.
Whomever picked these equations knew their onions I will tell you that. I went through the entire Sturmfels book and got nothing. One of the worst math books I have ever seen.
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.