1. **State the problem:** Sera buys 7 bunches of bananas, each bunch having either 4 or 5 bananas, totaling 31 bananas. We define $x$ as the number of bunches with 4 bananas and $y$ as the number of bunches with 5 bananas. 2. **Write the system of equations:** - The total number of bananas is given by $$4x + 5y = 31$$ - The total number of bunches is $$x + y = 7$$ 3. **Explanation:** - Each bunch with 4 bananas contributes $4x$ bananas. - Each bunch with 5 bananas contributes $5y$ bananas. - The sum of these must be 31. - The total number of bunches $x + y$ must be 7. 4. **Check other options:** - The system $$5x + 4y = 31, x + y = 7$$ swaps the coefficients incorrectly. - The systems with right sides 7 and 31 swapped are incorrect because the total bananas must be 31, and total bunches must be 7. **Final answer:** $$\begin{cases} 4x + 5y = 31 \\ x + y = 7 \end{cases}$$