1) $m=9→\begin{cases}3x+2y=10\\2x-y=9\end{cases}\\↔\begin{cases}3x+2y=10(1)\\4x-2y=18\end{cases}(2)\\(1)+(2)→3x+2y+4x-2y=10+18\\↔7x=28\\↔x=4\\→y=-1$
Vậy hpt có nghiệm $(x;y)=(4;-1)$
2) $\begin{cases}3x+2y=10\\2x-y=m\end{cases}$
$2x-y=m↔y=2x-m$
Thay $y=2x-m$ vào pt $3x+2y=10$
$→3x+2(2x-m)=10\\↔3x+4x-2m=10\\↔7x=2m+10\\↔x=\dfrac{2m+10}{7}\\→y=2.\dfrac{2m+10}{7}-m\\=\dfrac{4m+20-7m}{7}\\=\dfrac{20-3m}{7}$
Để hpt có nghiệm $x>0,y<0$
$→\begin{cases}\dfrac{2m+10}{7}>0\\\dfrac{20-3m}{7}<0\end{cases}\\↔\begin{cases}2m+10>0\\20-3m<0\end{cases}\\↔\begin{cases}2m>-10\\3m>20\end{cases}\\↔\begin{cases}m>-5\\m>\dfrac{20}{3}\end{cases}\\↔m>\dfrac{20}{3}$
Vậy $m>\dfrac{20}{3}$ thì hpt có nghiệm $x>0,y<0$
