\(\left\{{}\begin{matrix}\left(m-1\right)x-my=3m-1\\2x-y=m+5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=2x-m-5\\x\left(m-1\right)-m\left(2x-m-5\right)=3m-1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}mx-x-2mx+m^2+5m-3m+1=0\\y=2x-m-5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}-mx-x-m^2-8m+1=0\\y=2x-m-5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\left(m+1\right)=-m^2-8m+1\\y=2x-m-5\end{matrix}\right.\)
+) Nếu \(m=-1\) thì hệ vô nghiệm.
+) Nếu \(m\ne-1\) thì hệ có nghiệm duy nhất:
\(\left\{{}\begin{matrix}x=\frac{-m^2-8m+1}{m+1}\\y=\frac{2\left(-m^2-8m+1\right)}{m+1}-m-5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\frac{-m^2-8m+1}{m+1}\\y=\frac{-3m^2-22m-3}{m+1}\end{matrix}\right.\)
Vậy...
@Nguyễn Ngọc Lộc
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