\(\Leftrightarrow\left\{{}\begin{matrix}x^2-3xy-4y=0\left(1\right)\\y^2-3xy-4x=0\left(2\right)\end{matrix}\right.\)
ta lấy (1)-(2)\(\Leftrightarrow x^2-3xy-4y-\left(y^2-3xy-4x\right)=0\)
\(\Leftrightarrow x^2-y^2-4y+4x=0\)
\(\Leftrightarrow\left(x-y\right)\left(x+y\right)+4\left(x-y\right)=0\)
\(\Leftrightarrow\left(x-y\right)\left(x+y+4\right)=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=y\left(3\right)\\x=-y-4\left(4\right)\end{matrix}\right.\)
từ (1)(3) ta có hệ \(\Leftrightarrow\left\{{}\begin{matrix}x=y\\x^2-3xy-4y=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=y\\x^2-3xx-4x=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=y\\-2x^2-4x=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=y\\\left[{}\begin{matrix}x=0\\x=-2\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=0\\y=0\end{matrix}\right.\\\left\{{}\begin{matrix}x=-2\\y=-2\end{matrix}\right.\end{matrix}\right.\)
từ (1)(4) ta có hệ \(\Leftrightarrow\left\{{}\begin{matrix}x=-y-4\\x^2-3xy-4y=0\end{matrix}\right.\)
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