Đáp án:
m>1
Giải thích các bước giải:
\(\begin{array}{l}
\left\{ \begin{array}{l}
mx - y = 1\\
\left( {m + 1} \right)x + y = 2
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\left( {m + 1 + m} \right)x = 3\\
y = mx - 1
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{3}{{2m + 1}}\\
y = m.\dfrac{3}{{2m + 1}} - 1
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{3}{{2m + 1}}\\
y = \dfrac{{3m - 2m - 1}}{{2m + 1}}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{3}{{2m + 1}}\\
y = \dfrac{{m - 1}}{{2m + 1}}
\end{array} \right.\\
DK:m \ne - \dfrac{1}{2}\\
Do:x > 0;y > 0\\
\to \left\{ \begin{array}{l}
\dfrac{3}{{2m + 1}} > 0\\
\dfrac{{m - 1}}{{2m + 1}} > 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
2m + 1 > 0\\
m - 1 > 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
m > - \dfrac{1}{2}\\
m > 1
\end{array} \right.\\
\to m > 1
\end{array}\)
