1. **State the problem:** Determine which systems of equations are equivalent to the system: $$\begin{cases} y = -5x - 8 \end{cases}$$ 2. **Recall equivalency rules:** Two systems are equivalent if they have the same solution set. This means each equation in one system can be transformed into an equation in the other system by algebraic manipulation. 3. **Analyze each option:** - Option 1: $$\begin{cases} 3y = -11x - 4 \\ y = -3x + 2 \end{cases}$$ Check if either equation matches or is equivalent to $y = -5x - 8$. - For $3y = -11x - 4$, divide both sides by 3: $$y = -\frac{11}{3}x - \frac{4}{3}$$ This is not equal to $y = -5x - 8$. - The second equation is $y = -3x + 2$, which is different. So, Option 1 is **not equivalent**. - Option 2: $$\begin{cases} y = -8x - 6 \\ y = -5x - 8 \end{cases}$$ The second equation matches the original system exactly. - Option 3: $$\begin{cases} y = -3x + 2 \\ 2y = -8x - 6 \end{cases}$$ Rewrite $2y = -8x - 6$ as: $$y = -4x - 3$$ Neither equation matches $y = -5x - 8$. - Option 4: $$\begin{cases} 3y = -9x + 6 \\ y = -5x - 8 \end{cases}$$ Divide $3y = -9x + 6$ by 3: $$y = -3x + 2$$ The second equation matches the original system. 4. **Conclusion:** - The original system is $y = -5x - 8$. - Option 2 contains $y = -5x - 8$. - Option 4 contains $y = -5x - 8$ and $y = -3x + 2$ (which is different). Only Option 2 is equivalent to the original system. **Final answer:** Only the system in Option 2 is equivalent to the original system.