Question

\(\left\{{}\begin{matrix}2x+y=m\\3x-2y=5\end{matrix}\right.\) (m tham số)

Tìm m để hệ có nghiệm duy nhất (x;y) thỏa mãn x>0 ; y<0

Answer 1

\(\left\{{}\begin{matrix}2x+y=m\\3x-2y=5\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}4x+2y=2m\\3x-2y=5\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}7x=2m+5\\y=m-2x\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{2m+5}{7}\\y=\dfrac{3m-10}{7}\end{matrix}\right.\)

Để \(x>0;y< 0\Rightarrow\left\{{}\begin{matrix}\dfrac{2m+5}{7}>0\\\dfrac{3m-10}{7}< 0\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}m>-\dfrac{5}{2}\\m< \dfrac{10}{3}\end{matrix}\right.\) \(\Rightarrow-\dfrac{5}{2}< m< \dfrac{10}{3}\)