Question

Giải phương trình:

\(\left\{{}\begin{matrix}\frac{1}{x}+\frac{1}{y}=\frac{1}{6}\\\frac{2}{x}+\frac{3}{y}=\frac{2}{5}\end{matrix}\right.\)

Answer 1

Đặt \(\frac{1}{x}=u;\frac{1}{y}=v\)

\(hpt\Leftrightarrow\left\{{}\begin{matrix}u+v=\frac{1}{6}\\2u+3v=\frac{2}{5}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2u+2v=\frac{1}{3}\\2u+3v=\frac{2}{5}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}v=\frac{1}{15}\\u+v=\frac{1}{6}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}v=\frac{1}{15}\\u=\frac{1}{6}-v=\frac{1}{6}-\frac{1}{15}=\frac{1}{10}\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=10\\y=15\end{matrix}\right.\)