World Tour Germoney05

Algebra Level 5

\[\large{\begin{cases} x^{3}+1-xy^{2}-y^{2} =0 \\ y^{3}+1-yx^{2}-x^{2} =0 \end{cases}}\]

Find the number of pairs of real solutions \((x,y)\) that satisfy the system of equations above.

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