Question

giải hpt sau:

\(\left\{{}\begin{matrix}\\\end{matrix}\right.\dfrac{x+my=m+1}{mx+y=3m-1}\)

Answer 1

\(PT\left(1\right)\Leftrightarrow x=m+1-my\\ PT\left(2\right)\Leftrightarrow m^2+m-m^2y+y=3m-1\\ \Leftrightarrow y\left(1-m^2\right)=-m^2+2m-1\\ \Leftrightarrow y=\dfrac{\left(m-1\right)^2}{\left(m-1\right)\left(m+1\right)}=\dfrac{m-1}{m+1}\\ \Leftrightarrow x=m+1-\dfrac{m\left(m-1\right)}{m+1}=\dfrac{m^2+2m+1-m^2+m}{m+1}=\dfrac{3m+1}{m+1}\)

Vậy \(\left(x;y\right)=\left(\dfrac{3m+1}{m+1};\dfrac{m-1}{m+1}\right)\)