A software development team works on two projects simultaneously. In the first project, the team of 3 programmers and 2 designers must deliver 15 software modules. In the second project, the team of 2 programmers and 3 designers must deliver 10 software modules. If we know that both projects are completed at the same time, how many software modules should each team deliver?

Let's denote the number of software modules delivered by the first team of programmers and designers as "x" and the number of software modules delivered by the second team as "y". From the given information, we can set up the following equations: Equation 1: 3x + 2y = 15 This equation represents the number of software modules delivered by the first team (3x) and the second team (2y) in the first project, which must sum up to 15 modules. Equation 2: 2x + 3y = 10 This equation represents the number of software modules delivered by the first team (2x) and the second team (3y) in the second project, which must sum up to 10 modules. To find the values of "x" and "y," we can solve this system of equations. There are multiple methods to solve it, such as substitution or elimination. Here, we'll use the elimination method. Multiplying Equation 1 by 3 and Equation 2 by 2, we get: Equation 3: 9x + 6y = 45 Equation 4: 4x + 6y = 20 Subtracting Equation 4 from Equation 3, we eliminate the "y" term: (9x + 6y) - (4x + 6y) = 45 - 20 9x - 4x = 25 5x = 25 x = 25/5 x = 5 Now, substitute the value of "x" into either Equation 1 or Equation 2. Let's use Equation 1: 3x + 2y = 15 3(5) + 2y = 15 15 + 2y = 15 2y = 15 - 15 2y = 0 y = 0/2 y = 0 Therefore, the first team should deliver 5 software modules (x = 5), and the second team should deliver 0 software modules (y = 0) to complete both projects simultaneously.