Write a system of equations to represent the volume of each box, \( y \). Which statement describes the number and viability of the sy: solutions? A. The system has only one solution, and it is viable because it results in positive side lengths. B. The system has two solutions, but only one is viable because the other results in negative side lengths. C. The system has only one solution, but it is not viable because it results in negative side lengths. D. The system has two solutions, and both are viable because they result in positive side lengths.

To determine the correct statement about the system of equations representing the volume of each box, let's analyze the typical scenario involving box dimensions and volume. **Assumptions:** - Let's assume that the box has dimensions such as length, width, and height, and the volume \( y \) is given by the product of these dimensions. - When setting up the system of equations, you might end up with a quadratic equation after substituting and simplifying, especially if you're solving for one dimension in terms of the others. **Possible Outcomes:** 1. **One Solution:** If the system simplifies to a linear equation, there would be a single solution. However, this is less common when dealing with volume equations that are often quadratic in nature. 2. **Two Solutions:** More commonly, quadratic equations yield two solutions. However, in the context of physical dimensions: - **Viable Solution:** Positive side lengths are required for a real, physical box. - **Non-viable Solution:** Negative side lengths do not make sense in real-world scenarios. **Conclusion:** Given that quadratic systems typically produce two solutions but only one makes physical sense (positive dimensions), the most accurate statement is: **Answer:** B. The system has two solutions, but only one is viable because the other results in negative side lengths.