Question

Giải hệ phương trình: \(\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{5}{24}\\\dfrac{9}{x}+\dfrac{6}{5}\left(\dfrac{1}{x}+\dfrac{1}{y}\right)=1\end{matrix}\right.\)

Answer 1

\(\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{5}{24}\\\dfrac{9}{x}+\dfrac{6}{5}\left(\dfrac{1}{x}+\dfrac{1}{y}\right)=1\end{matrix}\right.\)

\(\Rightarrow\dfrac{9}{x}+\dfrac{6}{5}.\dfrac{5}{24}=1\)

\(\Leftrightarrow\dfrac{9}{x}+\dfrac{1}{4}=1\)

\(\Leftrightarrow\dfrac{9}{x}=\dfrac{3}{4}\)

\(\Leftrightarrow3x=36\Leftrightarrow x=12\)

\(\Rightarrow\dfrac{1}{12}+\dfrac{1}{y}=\dfrac{5}{24}\)

\(\Rightarrow\dfrac{1}{y}=\dfrac{1}{8}\Rightarrow y=8\)

Vậy x = 12, y = 8