[TEX]\[\begin{array}{l}\left\{ \begin{array}{l}{x^4} - {x^3}y + {x^2}{y^2} - 1 = 0\\{x^3}y - {x^2} + xy + 1 = 0\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}{x^4} - {x^3}y + {x^2}{y^2} - 1 + 2\left( {{x^3}y - {x^2} + xy + 1} \right) = 0\\{x^3}y - {x^2} + xy + 1 = 0\end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l}{\left( {{x^2} - xy - 1} \right)^2} + 3{x^3}y = 0\\{x^3}y - {x^2} + xy + 1 = 0\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}{\left( {{x^2} - xy - 1} \right)^2} + 3\left( {{x^2} - xy - 1} \right) = 0\\{x^3}y - {x^2} + xy + 1 = 0\end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l}{x^2} - xy - 1 = 0\\{x^3}y = 0\end{array} \right. \vee \left\{ \begin{array}{l}{x^2} - xy - 1 = - 3\\{x^3}y = - 3\end{array} \right.\end{array}[/TEX]
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