\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Apply successively the swap \(L_1 \leftrightarrow L_2\) and the dilation \(L_1 \leftarrow \tfrac{1}{2} L_1\) to the augmented matrix \(\left( \begin{array}{cc|c} 4 & 6 & 8 \\ 1 & 1 & 3 \end{array} \right)\). State the row-equivalent system at each step.
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