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 dissect this scenario, let’s imagine that you have two boxes, with dimensions represented by different sets of equations. For instance, you might have equations like \( xy = V_1 \) and \( xz = V_2 \), where \( V_1 \) and \( V_2 \) are volumes of the boxes, and \( x, y, z \) are the side lengths. Depending on how you set these up, you can arrive at one unique solution or multiple solutions that are either viable or not based on the physical constraints of box dimensions. In practical terms, if you were to graph these equations, the intersection points of the lines (or surfaces, in three dimensions) would indicate potential solutions. If these points yield negative dimensions, that’s a hard no for viability. Therefore, if it’s down to one solution and yields positive dimensions, option A stands strong! But if you find two positive viable solutions, you’d cheer for D. Choose wisely!