Ta có : \(\left\{{}\begin{matrix}mx+y=3\\4x+my=6\end{matrix}\right.\)
=> \(\left\{{}\begin{matrix}y=3-mx\\4x+m\left(3-mx\right)=6\end{matrix}\right.\)
=> \(\left\{{}\begin{matrix}y=3-mx\\4x+3m-m^2x=6\end{matrix}\right.\)
=> \(\left\{{}\begin{matrix}y=3-mx\\x=\frac{6-3m}{4-m^2}\end{matrix}\right.\)
=> \(\left\{{}\begin{matrix}y=3-\frac{3m}{m+2}=\frac{3m+6-3m}{m+2}=\frac{6}{m+2}\\x=\frac{6-3m}{4-m^2}=\frac{3m-6}{m^2-4}=\frac{3\left(m-2\right)}{\left(m-2\right)\left(m+2\right)}=\frac{3}{m+2}\end{matrix}\right.\)
- Ta có : \(\left\{{}\begin{matrix}x>2\\y>0\end{matrix}\right.\)
=> \(\left\{{}\begin{matrix}\frac{3}{m+2}>2\\\frac{6}{m+2}>0\end{matrix}\right.\)
=> \(\left\{{}\begin{matrix}\frac{3}{m+2}-2=\frac{3-2m-4}{m+2}>0\\\frac{6}{m+2}>0\end{matrix}\right.\)
=> \(\left\{{}\begin{matrix}3-2m-4>0\\m+2>0\end{matrix}\right.\)
=> \(\left\{{}\begin{matrix}2m+1< 0\\m+2>0\end{matrix}\right.\)
=> \(\left\{{}\begin{matrix}m< -\frac{1}{2}\\m>-2\end{matrix}\right.\)
=> \(-2< m< -\frac{1}{2}\)
Vậy ....
