1.
\(\left\{{}\begin{matrix}mx-y=2\\3x+my=5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=mx-2\\3x+m\left(mx-2\right)=5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}3x+xm^2-2m=5\\y=mx-2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\left(m^2+3\right)=2m+5\\y=mx-2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\frac{2m+5}{m^2+3}\\y=\frac{m\left(2m+5\right)}{m^2+3}-2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\frac{2m+5}{m^2+3}\\y=\frac{5m-6}{m^2+3}\end{matrix}\right.\)
Khi đó: \(x+y=1-\frac{m^2}{m^2+3}\)
\(\Leftrightarrow\frac{2m+5}{m^2+3}+\frac{5m-6}{m^2+3}=1-\frac{m^2}{m^2+3}\)
\(\Leftrightarrow\frac{7m-4}{m^2+3}=0\)
\(\Leftrightarrow7m-4=0\)
\(\Leftrightarrow m=\frac{4}{7}\)
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2.
\(\left\{{}\begin{matrix}2x+y=a+2\\x-y=a\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=a+y\\2a+2y+y=a+2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}3y=-a+2\\x=a+y\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=\frac{-a+2}{3}\\x=a+\frac{-a+2}{3}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=\frac{-a+2}{3}\\x=\frac{2a+2}{3}\end{matrix}\right.\)
\(x< y\Leftrightarrow\frac{2a+2}{3}< \frac{-a+2}{3}\)
\(\Leftrightarrow\frac{2a+2+a-2}{3}< 0\)
\(\Leftrightarrow\frac{3a}{3}< 0\)
\(\Leftrightarrow a< 0\)
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