Question

\(\left\{{}\begin{matrix}2x-my=-3\\mx+3y=4\end{matrix}\right.\) Tìm m để pt có nghiệm (x;y) thỏa mãn x<0,y>0

Answer 1

\(\left\{{}\begin{matrix}6x-3my=-9\\m^2x+3my=4m\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}6x-3my=-9\\\left(m^2+6\right)x=4m-9\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x=\frac{4m-9}{m^2+6}\\y=\frac{3m+8}{m^2+6}\end{matrix}\right.\)

\(\left\{{}\begin{matrix}x< 0\\y>0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}\frac{4m-9}{m^2+6}< 0\\\frac{3m+8}{m^2+6}>0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}m< \frac{9}{4}\\m>-\frac{8}{3}\end{matrix}\right.\)

\(\Rightarrow-\frac{8}{3}< m< \frac{9}{4}\)