\(hpt:\left\{{}\begin{matrix}x-2y=0\\mx-3y=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2y\\mx-3y=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2y\\2my-3y=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2y\\y\left(2m-3\right)=2\end{matrix}\right.\left(I\right)\)
Để hpt có nghiệm thì:
\(2m-3\ne0\Leftrightarrow m\ne\frac{3}{2}\)
\(hpt\left(I\right)\Leftrightarrow\left\{{}\begin{matrix}x=2y\\y=\frac{2}{2m-3}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\frac{4}{2m-3}\\y=\frac{2}{2m-3}\end{matrix}\right.\)
Để hpt có nghiệm dương thì:
\(\left\{{}\begin{matrix}\frac{4}{2m-3}>0\\\frac{2}{2m-3}>0\end{matrix}\right.\Rightarrow2m-3>0\Leftrightarrow m>\frac{3}{2}\)