Ta có: \(\dfrac{7}{15x}+\dfrac{9}{10y}=\dfrac{2}{5}-\dfrac{359}{30xy}\)
\(\Leftrightarrow\dfrac{14}{30xy}+\dfrac{27}{30xy}=\dfrac{12xy}{30xy}-\dfrac{359}{30xy}\)
\(\Leftrightarrow\dfrac{41}{30xy}=\dfrac{12xy-359}{30xy}\)
\(\Rightarrow12xy-359=41\)
\(\Rightarrow12xy=400\)
\(\Rightarrow xy=\dfrac{100}{3}\)
Vì \(x,y\in Z\) mà \(xy=\dfrac{100}{3}\)
\(\Rightarrow\) Phương trình vô nghiệm.