1)    a) Khi \(m = 3 \Rightarrow \left\{ \begin{array}{l}x + 3y = 2\\2x + 4y = 3\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}x = \frac{1}{2}\\y = \frac{1}{2}\end{array} \right.\)

\(b)\left\{ \begin{array}{l}x + my = 2\\2x + 4y = 3\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}2x + 2my = 4\\2x + 4y = 3\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}y = \frac{1}\\x = \frac}}{2} = \frac{{2\left( {3m - 8} \right)}}\end{array} \right.\)

Để \(x,y\)đối nhau thì :

\( \Rightarrow \frac{{2\left( {3m - 8} \right)}} = \frac{{ - 1}} \Leftrightarrow \left( {6m - 16} \right).2 = - 1 \Leftrightarrow 12m = 31 \Leftrightarrow m = \frac\)

2)    Hoành độ \(A,B\)là nghiệm hệ \( - {x^2} = x - 2 \Leftrightarrow {x^2} + x - 2 = 0\)

\( \Rightarrow \left[ \begin{array}{l}{x_A} = 1 \Rightarrow {y_A} = - 1\\{x_B} = - 2 \Rightarrow {y_B} = - 4\end{array} \right. \Rightarrow A\left( {1; - 1} \right);B\left( { - 2; - 4} \right),O\left( {0;0} \right)\)

vuông tại A