Question

\(\left\{{}\begin{matrix}2x+3y=-xy\\\dfrac{8}{y}-\dfrac{6}{x}=5\end{matrix}\right.\)

Answer 1

ĐKXĐ: \(xy\ne0\)

\(\left\{{}\begin{matrix}2x+3y=-xy\\\dfrac{8}{y}-\dfrac{6}{x}=5\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}\dfrac{2}{y}+\dfrac{3}{x}=-1\\\dfrac{8}{y}-\dfrac{6}{x}=5\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{4}{y}+\dfrac{6}{x}=-2\\\dfrac{8}{y}-\dfrac{6}{x}=5\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{12}{y}=3\\\dfrac{8}{y}-\dfrac{6}{x}=5\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}\dfrac{1}{y}=\dfrac{1}{4}\\\dfrac{1}{x}=-\dfrac{1}{2}\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x=-2\\y=4\end{matrix}\right.\)