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Prove solutions of system

Source: Cono Sur 1991-problem 3

May 29, 2006
algebra unsolvedalgebra

Problem Statement

It is known that the number of real solutions of the following system if finite. Prove that this system has an even number of solutions: (y2+6)(x−1)=y(x2+1)(y^2+6)(x-1)=y(x^2+1) (x2+6)(y−1)=x(y2+1)(x^2+6)(y-1)=x(y^2+1)
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