\(\left\{{}\begin{matrix}\dfrac{24}{5x}+\dfrac{24}{5y}=1\\x=y-4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=1:\dfrac{24}{5}=\dfrac{5}{24}\\x=y-4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{1}{y-4}+\dfrac{1}{y}=\dfrac{5}{24}\\x=y-4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{y+y-4}{y\left(y-4\right)}=\dfrac{5}{24}\\x=y-4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}5y\left(y-4\right)=24\left(2y-4\right)\\x=y-4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5y^2-20y-48y+96=0\\x=y-4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}5y^2-68y+96=0\\x=y-4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left(y-12\right)\left(5y-8\right)=0\\x=y-4\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}\left\{{}\begin{matrix}y-12=0\\x=y-4\end{matrix}\right.\\\left\{{}\begin{matrix}5y-8=0\\x=y-4\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}y=12\\x=12-4=8\end{matrix}\right.\\\left\{{}\begin{matrix}y=\dfrac{8}{5}\\x=\dfrac{8}{5}-4=-\dfrac{12}{5}\end{matrix}\right.\end{matrix}\right.\)
