\(\left\{{}\begin{matrix}6x+5y=2xy\\20x-20y-xy=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}6x+5y=2xy\\40x-40y=2xy\end{matrix}\right.\Leftrightarrow6x+5y=40x-40y\)
=>-34x=-45y
=>\(\dfrac{x}{45}=\dfrac{y}{34}=k\)
=>x=45k; y=34k
6x+5y=2xy
=>\(6\cdot45k+5\cdot34k=2\cdot45k\cdot34k\)
=>\(3060k^2=440k\)
=>\(3060k^2-440k=0\)
=>k(3060k-440)=0
=>\(\left[{}\begin{matrix}k=0\\k=\dfrac{22}{153}\end{matrix}\right.\)
Khi k=0 thì \(\left\{{}\begin{matrix}x=45\cdot0=0\\y=34\cdot0=0\end{matrix}\right.\)
Khi \(k=\dfrac{22}{153}\) thì \(\left\{{}\begin{matrix}x=45\cdot\dfrac{22}{153}=\dfrac{990}{153}=\dfrac{110}{17}\\y=34\cdot\dfrac{22}{153}=\dfrac{44}{9}\end{matrix}\right.\)
\(\left\{{}\begin{matrix}6x+5y=2xy\\20x-20y-xy=0\end{matrix}\right.\\ < =>\left\{{}\begin{matrix}6x+5y=2xy\\40x-40y=2xy\end{matrix}\right.\\ < =>6x+5y=40x-40y\\ < =>34x=45y\\ < =>y=\dfrac{34x}{45}\)
