$\left\{{{2mx-(m+1)y=m-n}\atop{(m+2)x+3ny=2m-3}}\right.$
$\text{Vì hệ có nghiệm }(2; -1)$
$\Rightarrow \left\{{{4m-(m+1)(-1)=m-n}\atop{(m+2).2+3n.(-1)=2m-3}}\right.$
$\Leftrightarrow \left\{{{4m+m+1=m-n}\atop{2m+4-3n=2m-3}}\right.$
$\Leftrightarrow \left\{{{4m+n=-1}\atop{-3n=-7}}\right.$
$\Leftrightarrow \left\{{{4m+n=-1}\atop{n=\frac{7}{3}}}\right.$
$\Leftrightarrow \left\{{{m=\frac{-1-n}{4}}\atop{n=\frac{7}{3}}}\right.$
$\Leftrightarrow \left\{{{m=-\frac{5}{6}}\atop{n=\frac{7}{3}}}\right.$
$\Rightarrow (x; y)=(-\frac{5}{6}; \frac{7}{3})$