Ta có: \(\left\{{}\begin{matrix}\dfrac{81}{x}+\dfrac{105}{y}=8\\\dfrac{54}{x}+\dfrac{42}{y}=4\end{matrix}\right.\)
Đặt: \(u=\dfrac{54}{x}\Rightarrow\dfrac{81}{x}=1,5u\)
\(v=\dfrac{42}{y}\Rightarrow+\dfrac{105}{y}=2,5v\)
Hệ phương trình đã cho tương đương
\(\left\{{}\begin{matrix}1,5u+2,5v=8\\u+v=4\end{matrix}\right.\)
\(\Leftrightarrow\)\(\left\{{}\begin{matrix}1,5u+2,5v=8\\1,5u+1,5v=6\end{matrix}\right.\)
\(\Leftrightarrow\)\(\left\{{}\begin{matrix}v=2\\u+v=4\end{matrix}\right.\)
\(\Leftrightarrow\)\(\left\{{}\begin{matrix}v=2\\u=2\end{matrix}\right.\)
\(\Leftrightarrow\)\(\left\{{}\begin{matrix}x=27\\y=21\end{matrix}\right.\)
