HPT : \(\hept{\begin{cases}\frac{1}{x}+\frac{1}{y}=\frac{5}{36}\\\frac{4}{x}+\frac{3}{y}=\frac{1}{2}\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}\frac{3}{x}+\frac{3}{y}=\frac{5}{12}\left(1\right)\\\frac{4}{x}+\frac{3}{y}=\frac{1}{2}\left(2\right)\end{cases}}\)
Từ (1) và (2), lấy vế trừ vế ta được :
\(\Leftrightarrow\left(\frac{4}{x}+\frac{3}{y}\right)-\left(\frac{3}{x}+\frac{3}{y}\right)=\frac{1}{2}-\frac{5}{12}\)
\(\Leftrightarrow\frac{1}{x}=\frac{1}{12}\)
\(\Leftrightarrow\frac{1}{y}=\frac{5}{36}-\frac{1}{x}=\frac{5}{36}-\frac{1}{12}=\frac{1}{18}\)
\(\Leftrightarrow\hept{\begin{cases}x=12\\y=18\end{cases}}\)
