Question

\(\left\{{}\begin{matrix}12x+3y=4xy\\\dfrac{9}{x}-\dfrac{8}{y}=1\end{matrix}\right.\)

Answer 1

ĐKXĐ: \(xy\ne0\)

\(\left\{{}\begin{matrix}12x+3y=4xy\\\dfrac{9}{x}-\dfrac{8}{y}=1\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}\dfrac{3}{x}+\dfrac{12}{y}=4\\\dfrac{9}{x}-\dfrac{8}{y}=1\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{9}{x}+\dfrac{36}{y}=12\\\dfrac{9}{x}-\dfrac{8}{y}=1\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{44}{y}=11\\\dfrac{9}{x}-\dfrac{8}{y}=1\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}\dfrac{1}{y}=\dfrac{1}{4}\\\dfrac{1}{x}=\dfrac{1}{3}\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x=3\\y=4\end{matrix}\right.\)