Answer
\[ \left[\begin{array}{rr|r} 2 & 3 & 6 \\ 4 & -6 & -2 \\ \end{array} \right] \]
Work Step by Step
I modify the original equations in the form such that the constant "goes" onto the other side of the equality.
$2x+3y-6=0\\2x+3x=6$
$4x-6y+2=0\\4x-6y=-2$
We know that \[ \left\{ \begin{array}{c} a_1x+b_1y=c_1 \\ a_2x+b_2y=c_2 \\ \end{array} \right. \] becomes \[ \left[\begin{array}{rr|r} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ \end{array} \right] \] Hence here the augmented matrix is: \[ \left[\begin{array}{rr|r} 2 & 3 & 6 \\ 4 & -6 & -2 \\ \end{array} \right] \]
