\(\left\{{}\begin{matrix}\frac{4}{x}+\frac{4}{y}=\frac{1}{3}\\\frac{4}{x}+\frac{6}{y}=\frac{2}{5}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\frac{1}{x}+\frac{1}{y}=\frac{1}{12}\\\frac{2}{y}=\frac{2}{5}-\frac{1}{3}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\frac{1}{x}+\frac{1}{30}=\frac{1}{12}\\y=30\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\frac{60}{7}\\y=30\end{matrix}\right.\)
Đặt: a=\(\frac{1}{x}\), b=\(\frac{1}{y}\) ta có:
\(\left\{{}\begin{matrix}a+b=\frac{1}{12}\\4a+6b=\frac{2}{5}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}4a+4b=\frac{1}{3}\\4a+6b=\frac{2}{5}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}a+b=\frac{1}{12}\\-2b=-\frac{1}{15}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}a=\frac{1}{20}\\b=\frac{1}{30}\end{matrix}\right.\)
hay: \(\frac{1}{x}=\frac{1}{20}\Rightarrow x=20\)
\(\frac{1}{y}=\frac{1}{30}\Rightarrow y=30\)