\begin{tabular}{l} Stacy is solving the system of equations shown below: \\ \( 3 w+7 t=64 \) \\ \( 6 w+2 t=44 \) \\ Stacy correctly uses the elimination method to solve the system of equations. \\ Her first step is to rewrite one equation so one of the variables can be eliminated. \\ Which system of equations could show Stacy's rewritten system of equations? \\ \begin{tabular}{l}\( -6 w+-14 t=-128 \) \\ \( 6 w+2 t=44 \) \\ \( 3 w+7 t=64 \) \\ \( -3 w+-2 t=-22 \) \\ \hline\( -6 w+-10 t=-67 \) \\ \( 6 w+2 t=44 \) \\ \hline \( 3 w+7 t=64 \) \\ \( -42 w+-7 t=-308 \)\end{tabular} \\ \hline\end{tabular}

To correctly use the elimination method in solving the system of equations, Stacy needs to manipulate one of the equations to match the coefficients of either \(w\) or \(t\) for easy elimination. For instance, if Stacy multiplies the first equation \(3w + 7t = 64\) by -2, she will rewrite it as \(-6w - 14t = -128\). This modified equation can then be paired with the second equation \(6w + 2t = 44\) to eliminate the variable \(w\) by adding the two equations together. Moreover, it's crucial for students to double-check their modifications to ensure correctness. They might mistakenly alter coefficients or constants, leading to incorrect elimination or false solutions! It's a great reminder to keep an eye on negative signs during these transformations.