Solving systems of equations, receiving z and z1 in solution?

Question

I passed the following nonlinear system to Matlab:

2(x−p1)+2(xy−p3)y = 0
2(y−p2)+2(xy−p3)x = 0

and used syms to find solution for x and y symbolically but I got:

sol.x

ans =

(p1^3 + p3*p1^2*z1 + p1*z1^4 - 1.0*p2*p1*z1^3 + p1*z1^2 - 1.0*p2*p1*z1 + p3*z1^3 - 1.0*p2*p3*z1^2 + p3*z1 - 1.0*p2*p3)/(p1^2 + p3^2)

and

sol.y

ans =
z1
where z1 = RootOf(z^5 - p2*z^4 + 2*z^3 - z^2*(2*p2 - p1*p3) + z*(p1^2 - p3^2 + 1) - p1*p3 - p2, z)

I dont understand where z come from? what is z?

Answer 1

Your y solution is expressed in terms of roots of a polynomial in z that depends on your equation's parameters also.

To show why is difficult to answer your question in the present form, please allow me to rephrase it: the numbers I'm looking for are the roots of an equation f(z) = 0; now, where z comes from? :-)