Use NSolve for a system of two nonlinear equations two unknowns?

Questions
,
1

Dear Fellows,

I used NSolve to solve a nonlinear system of two equations with two unknowns as follows:

NSolve[{-2.9*(10^(-15))*(y-x)^2+x^2*(y-x)^2-x^4==0,-2.9*(10^(-15))*(y-x)^2+(y-x)^2*y^2+y^4==0},{x,y},20]

I expect to receive just 4 solutions for this system of equations. However, mathematica provides a lot of solutions including 4 real and 4 complex solutions. I can reproduce the real solutions (almost similar) with FindRoot command of Mathematica.
Would some body plz hint me how these complex solutions are found?
Isn’t NSolve supposed to return only 4 solutions for a fourth order equation totally?

2

they’re fourth order in two variables

3

Bezout’s theorem allows for as many as 4*4 = 16 solutions (product of total degrees). So 14, which is what I see in version 11.3, is certainly plausible.