\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Apply the transvection \(L_2 \leftarrow L_2 - 3 L_1\) to the augmented matrix \(\left( \begin{array}{cc|c} 1 & 4 & 2 \\ 3 & 7 & 5 \end{array} \right)\) and verify that the new system has the same solutions as the original.
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