Question

giải hệ sau : \(\left\{{}\begin{matrix}xy=1\\x+3y=-22\\2x+2y=-16\end{matrix}\right.\)

Answer 1

Ta có:

\(\left\{{}\begin{matrix}xy=1\\x+3y=-22\\2x+2y=-16\end{matrix}\right.\)

\(\)\(\left\{{}\begin{matrix}xy=1\\2x+6y=-44\\2x+2y=-16\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}xy=1\\4y=-28\\x+3y=-22\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left(-7\right)x=1\\y=-7\\x+3.\left(-7\right)=-22\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{-1}{7}\\y=-7\\x=-1\end{matrix}\right.\)(vô lý)

Vậy hệ phương trình vô nghiệm.