Tim cac gia tri nguyen cua m de he: 2x + y = m 3x – 2y = 5 co nghiem x > 0, y > 0.

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1. Đáp án:

   $\begin{array}{l}
   \left\{ \begin{array}{l}
   2x + y = m\\
   3x – 2y = 5
   \end{array} \right.\\
    \Rightarrow \left\{ \begin{array}{l}
   4x + 2y = 2m\\
   3x – 2y = 5
   \end{array} \right.\\
    \Rightarrow \left\{ \begin{array}{l}
   7x = 2m + 5\\
   y = m – 2x
   \end{array} \right.\\
    \Rightarrow \left\{ \begin{array}{l}
   x = \dfrac{{2m + 5}}{7}\\
   y = m – 2.\dfrac{{2m + 5}}{7}
   \end{array} \right.\\
    \Rightarrow \left\{ \begin{array}{l}
   x = \dfrac{{2m + 5}}{7}\\
   y = \dfrac{{3m – 10}}{7}
   \end{array} \right.\\
   x > 0;y > 0\\
    \Rightarrow \left\{ \begin{array}{l}
   \dfrac{{2m + 5}}{7} > 0\\
   \dfrac{{3m – 10}}{7} > 0
   \end{array} \right.\\
    \Rightarrow \left\{ \begin{array}{l}
   2m + 5 > 0\\
   3m – 10 > 0
   \end{array} \right.\\
    \Rightarrow \left\{ \begin{array}{l}
   m >  – \dfrac{5}{2}\\
   m > \dfrac{{10}}{3}
   \end{array} \right.\\
    \Rightarrow m > \dfrac{{10}}{3}
   \end{array}$

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