TH1 \(m=0\Rightarrow\hept{\begin{cases}-y=2\\3x=5\end{cases}\Rightarrow\hept{\begin{cases}y=-2\\x=\frac{5}{3}\end{cases}\left(l\right)}}\)
TH2 \(m\ne0\)
Hệ pt \(\Leftrightarrow\hept{\begin{cases}m^2x-my=2m\\3x+my=5\end{cases}}\)
\(\Rightarrow m^2x+3x=2m+5\Rightarrow\left(m^2+3\right)x=2m+5\)
\(\Rightarrow x=\frac{2m+5}{m^2+3}\)
\(\Rightarrow y=mx-2=m.\frac{2m+5}{m^2+3}-2=\frac{2m^2+5m-2m^2-6}{m^2+3}\)
\(=\frac{5m-6}{m^2+3}\)
Yêu cầu bài toán \(\Leftrightarrow\hept{\begin{cases}x>0\\y>0\end{cases}\Leftrightarrow\hept{\begin{cases}\frac{2m+5}{m^2+3}>0\\\frac{5m-6}{m^2+3}>0\end{cases}}}\)
\(\Leftrightarrow\hept{\begin{cases}m>\frac{6}{5}\\m>-\frac{5}{2}\end{cases}\Leftrightarrow m>\frac{6}{5}}\)
Vậy m=6/5
