\(\Leftrightarrow\left\{{}\begin{matrix}y=3m-1-mx\\x+m\left(3m-1-mx\right)=m+1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=-mx+3m-1\\x+3m^2-m-m^2x=m+1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=-mx+3m-1\\x\left(1-m^2\right)=m+1-3m^2+m=-2m^2+m+1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=-mx-3m+1\\x\left(m-1\right)\left(m+1\right)=2m^2-m-1=\left(m-1\right)\left(2m+1\right)\end{matrix}\right.\)
Nếu m=1 thì hệ có vô số nghiệm
Nếu m=-1 thì hệ vô nghiệm
Nếu m<>1; m<>-1 thì hệ có nghiệm duy nhất là:
\(\left\{{}\begin{matrix}x=\dfrac{2m+1}{m+1}\\y=-m\cdot\dfrac{2m+1}{m+1}-3m+1=\dfrac{-2m^2-m+\left(-3m+1\right)\left(m+1\right)}{m+1}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{2m+1}{m+1}\\y=\dfrac{-2m^2-m-3m^2-3m+m+1}{m+1}=\dfrac{-5m^2-3m+1}{m+1}\end{matrix}\right.\)
