A pair of equations.

Algebra Level 4

How many ordered pairs of real numbers (x,y) (x,y) satisfy: (x1)(y2+6)=y(x2+1),(x-1)(y^{2}+6)= y(x^{2}+1), (y1)(x2+6)=x(y2+1)?(y-1)(x^{2}+6)=x(y^{2}+1)?

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