Question

Giải hệ phương trình \(\left\{{}\begin{matrix}\frac{1}{x+1}+\frac{1}{y}=1\\3x-y=xy\end{matrix}\right.\)

Answer 1

\(\left\{{}\begin{matrix}\frac{1}{x+1}+\frac{1}{y}=1\\3x-y=xy\end{matrix}\right.\)(ĐK:\(x\ne-1;y\ne0\))

\(\Leftrightarrow\left\{{}\begin{matrix}y+x+1=xy+y\\3x=xy+y\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}y+x+1=3x\\3x=xy+y\end{matrix}\right.\)

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

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

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=\frac{\sqrt{3}+1}{2}\\y=\sqrt{3}\end{matrix}\right.\\\left\{{}\begin{matrix}x=\frac{-\sqrt{3}+1}{2}\\y=-\sqrt{3}\end{matrix}\right.\end{matrix}\right.\)