\(m=0\Rightarrow\left\{{}\begin{matrix}x=1\\y=-1\end{matrix}\right.\) \(\Rightarrow xy=-1\) (1)
\(m=\pm1\) hệ vô nghiệm
Với \(m\ne0;\pm1\Rightarrow\left\{{}\begin{matrix}mx+m^2y=m^2+m\\mx+y=3m-1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=\frac{3m+1}{m+1}\\y=\frac{m-1}{m+1}\end{matrix}\right.\)
\(\Rightarrow A=xy=\frac{\left(3m+1\right)\left(m-1\right)}{\left(m+1\right)^2}=\frac{-\left(m^2+2m+1\right)+4m^2}{\left(m+1\right)^2}=-1+\frac{4m^2}{\left(m+1\right)^2}\ge-1\) (2)
Từ (1); (2) \(\Rightarrow xy_{min}=-1\) khi \(m=0\)