Đáp án:
\(\left[ \begin{array}{l}
m = - 1\\
m = - 3
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
\left\{ \begin{array}{l}
x + y = m + 2\\
3x + 5y = 2m
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = m + 2 - y\\
3\left( {m + 2 - y} \right) + 5y = 2m
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = m + 2 - y\\
3m + 6 - 3y + 5y = 2m
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = m + 2 - y\\
2y = - m - 6
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = \frac{{ - m - 6}}{2}\\
x = m + 2 + \frac{{m + 6}}{2}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = \frac{{ - m - 6}}{2}\\
x = \frac{{2m + 4 + m + 6}}{2}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = \frac{{ - m - 6}}{2}\\
x = \frac{{3m + 10}}{2}
\end{array} \right.\\
Để:\left| {x + y} \right| = 1\\
\to \left[ \begin{array}{l}
x + y = 1\\
x + y = - 1
\end{array} \right.\\
\to \left[ \begin{array}{l}
\frac{{3m + 10}}{2} + \frac{{ - m - 6}}{2} = 1\\
\frac{{3m + 10}}{2} + \frac{{ - m - 6}}{2} = - 1
\end{array} \right.\\
\to \left[ \begin{array}{l}
\frac{{3m + 10 - m - 6}}{2} = 1\\
\frac{{3m + 10 - m - 6}}{2} = - 1
\end{array} \right.\\
\to \left[ \begin{array}{l}
2m + 4 = 2\\
2m + 4 = - 2
\end{array} \right.\\
\to \left[ \begin{array}{l}
2m = - 2\\
2m = - 6
\end{array} \right.\\
\to \left[ \begin{array}{l}
m = - 1\\
m = - 3
\end{array} \right.
\end{array}\)
