\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}

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Stacy is solving the system of equations using the elimination method:

$$
\begin{cases}
3w + 7t = 64 \
6w + 2t = 44
\end{cases}
$$

**Elimination Method Steps:**

1. **Choose a Variable to Eliminate:** Let's choose to eliminate $$ w $$.
2. **Make the Coefficients of $$ w $$ Opposite:**
   - Multiply the first equation by $$-2$$ to make the coefficient of $$ w $$ equal to $$-6$$:
     $$
     -2(3w + 7t) = -2(64) \implies -6w - 14t = -128
     $$
   - The second equation remains unchanged:
     $$
     6w + 2t = 44
     $$
3. **Rewrite the System:**
   $$
   \begin{cases}
   -6w - 14t = -128 \
   6w + 2t = 44
   \end{cases}
   $$
   
By rewriting the system this way, Stacey can add the two equations to eliminate $$ w $$:
$$
(-6w - 14t) + (6w + 2t) = -128 + 44 \implies -12t = -84 \implies t = 7
$$

**Answer:**

$$
\begin{cases}
-6w - 14t = -128 \
6w + 2t = 44
\end{cases}
$$
Stacy's rewritten system of equations is: $$ \begin{cases} -6w - 14t = -128 \ 6w + 2t = 44 \end{cases} $$

Stacy is solving the system of equations shown below:

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?

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Stacy is solving the system of equations shown below: 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?