\(\left\{{}\begin{matrix}mx-y=2\\x+my=3\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=mx-2\\x+m\left(mx-2\right)=3\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=mx-2\\x+m^2x-2m=3\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=mx-2\\x\left(m^2+1\right)=3+2m\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=m.\dfrac{3+2m}{m^2+1}-2\\x=\dfrac{3+2m}{m^2+1}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{3m+2m^2-2m^2-2}{m^2+1}\\x=\dfrac{3+2m}{m^2+1}\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{3m-2}{m^2+1}\\x=\dfrac{3+2m}{m^2+1}\end{matrix}\right.\)
\(x+y=0\\ \Leftrightarrow\dfrac{3m-2}{m^2+1}+\dfrac{3+2m}{m^2+1}=0\\ \Leftrightarrow\dfrac{3m-2+3+2m}{m^2+1}=0\\ \Rightarrow4m+1=0\\ \Leftrightarrow m=-\dfrac{1}{4}\)
x+y=0 \(\Rightarrow\) y=-x.
\(\left\{{}\begin{matrix}mx-y=2\\x+my=3\end{matrix}\right.\) \(\Rightarrow\) \(\left\{{}\begin{matrix}mx+x=2\\x-mx=3\end{matrix}\right.\) \(\Rightarrow\) \(\left\{{}\begin{matrix}x\left(m+1\right)=2\\x\left(1-m\right)=3\end{matrix}\right.\) \(\Rightarrow\) \(\dfrac{2}{m+1}=\dfrac{3}{1-m}\) \(\Rightarrow\) m=-1/5 (nhận).
