\(\dfrac{x}{9}-\dfrac{3}{y}=\dfrac{1}{18}\)
\(\dfrac{x}{9}-\dfrac{1}{18}=\dfrac{3}{y}\)
\(\dfrac{2x}{18}-\dfrac{1}{18}=\dfrac{3}{y}\)
\(\dfrac{2x-1}{18}=\dfrac{3}{y}\)
\(\Rightarrow\)(2x-1).y=18.3=54
54 có các ước là: \(\pm1;\pm2;\pm3;\pm6;\pm9;\pm18;\pm27;\pm54\)
*\(\left\{{}\begin{matrix}2x-1=1\\y=54\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}2x=2\\y=54\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=1\\y=54\end{matrix}\right.\)
*\(\left\{{}\begin{matrix}2x-1=54\\y=1\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}2x=55\\y=1\end{matrix}\right.\)\(\notin\) N ( Loại)
*\(\left\{{}\begin{matrix}2x-1=2\\y=27\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}2x=3\\y=27\end{matrix}\right.\) \(\notin\) N ( Loại )
*\(\left\{{}\begin{matrix}2x-1=27\\y=2\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}2x=28\\y=2\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=14\\y=2\end{matrix}\right.\)
*\(\left\{{}\begin{matrix}2x-1=3\\y=18\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}2x=4\\y=18\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=2\\y=18\end{matrix}\right.\)
*\(\left\{{}\begin{matrix}2x-1=18\\y=3\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}2x=19\\y=3\end{matrix}\right.\)\(\notin\) N ( Loại )
*\(\left\{{}\begin{matrix}2x-1=6\\y=9\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}2x=7\\y=9\end{matrix}\right.\)\(\notin\) N ( Loại )
*\(\left\{{}\begin{matrix}2x-1=9\\y=6\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}2x=10\\y=6\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=5\\y=6\end{matrix}\right.\)
Vậy có các cặp (x,y) t/m đề bài là : (1,54) ; (14,2) ; (2,18) ; (5,6)