Đáp án:
\(\left[ \begin{array}{l}
m = 0\\
m = - 2
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
\left\{ \begin{array}{l}
2x + y = 5m - 1\\
x - 2y = 2
\end{array} \right.\\
\to \left\{ \begin{array}{l}
4x + 2y = 10m - 2\\
x - 2y = 2
\end{array} \right.\\
\to \left\{ \begin{array}{l}
5x = 10m\\
y = \dfrac{{x - 2}}{2}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = 2m\\
y = m - 1
\end{array} \right.\\
Có:{x^2} - 2{y^2} = - 2\\
\to 4{m^2} - 2{\left( {m - 1} \right)^2} = - 2\\
\to 4{m^2} - 2\left( {{m^2} - 2m + 1} \right) = - 2\\
\to 2{m^2} + 4m = 0\\
\to 2m\left( {m + 2} \right) = 0\\
\to \left[ \begin{array}{l}
m = 0\\
m = - 2
\end{array} \right.
\end{array}\)
