ĐKXĐ: x<>0 và y<>0
\(\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{6}\\y-x=9\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=x+9\\\dfrac{1}{x}+\dfrac{1}{x+9}=\dfrac{1}{6}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=x+9\\\dfrac{x+9+x}{x\left(x+9\right)}=\dfrac{1}{6}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=x+9\\x\left(x+9\right)=6\left(2x+9\right)\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=x+9\\x^2+9x-12x-54=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=x+9\\x^2-3x-54=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=x+9\\\left(x-9\right)\left(x+6\right)=0\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}\left\{{}\begin{matrix}x-9=0\\y=x+9\end{matrix}\right.\\\left\{{}\begin{matrix}x+6=0\\y=x+9\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=9\\y=9+9=18\end{matrix}\right.\\\left\{{}\begin{matrix}x=-6\\y=-6+9=3\end{matrix}\right.\end{matrix}\right.\)
