Ta có HPT : \(\hept{\begin{cases}\frac{1}{x}+\frac{1}{y}=\frac{1}{12}\\\frac{4}{x}+\frac{6}{y}=\frac{2}{5}\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}\frac{4}{x}+\frac{4}{y}=\frac{1}{3}\left(1\right)\\\frac{4}{x}+\frac{6}{y}=\frac{2}{5}\left(2\right)\end{cases}}\)
Lấy (2) trừ (1) , ta được:
\(\frac{4}{x}+\frac{6}{y}-\frac{4}{x}-\frac{4}{y}=\frac{2}{5}-\frac{1}{3}\)
\(\Leftrightarrow\frac{2}{y}=\frac{1}{15}\)
\(\Leftrightarrow y=30\)
Thay y = 30 vào (1), ta được:
\(\frac{1}{x}+\frac{1}{30}=\frac{1}{12}\)
\(\Leftrightarrow\frac{1}{x}=\frac{1}{20}\)
\(\Leftrightarrow x=20\)
Vậy \(\left(x;y\right)\in\left\{\left(20;30\right)\right\}\)
