\(\left\{{}\begin{matrix}2x-y=m+2\\x-2y=3m+4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}4x-2y=2m+4\\x-2y=3m+4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}4x-2y-x+2y=2m+4-3m-4\\x-2y=3m+4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}3x=-m\\x-2y=3m+4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{m}{3}\\-\dfrac{m}{3}-2y=3m+4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{m}{3}\\-2y=\dfrac{10}{3}m+4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{m}{3}\\y=\dfrac{-5}{3}m-2\end{matrix}\right.\)
Để \(x^2+y^2=10\)
\(\Leftrightarrow\left(\dfrac{-m}{3}\right)^2+\left(\dfrac{-5x}{3}-2\right)^2=10\)
\(\Leftrightarrow\dfrac{m^2}{9}+\dfrac{25m^2}{9}+\dfrac{20m}{3}+4=10\)
\(\Leftrightarrow\dfrac{26m^2}{9}+\dfrac{20m}{3}-6=0\)
\(\Leftrightarrow\dfrac{26m^2}{9}+\dfrac{60m}{9}-\dfrac{54}{9}=0\)
\(\Leftrightarrow26m^2+60m-54=0\)
\(\Leftrightarrow\left[{}\begin{matrix}m=-3\\m=\dfrac{9}{13}\end{matrix}\right.\)