Final answer:
To determine if the solution to system B is the same as system A, we compare the solutions of both systems. If the solutions are the same, then the solution to system B is the same as system A. If the solutions are different, they are not the same.
Step-by-step explanation:
In this question, we are given a system of equations called system A and we need to determine if the solution to system B, which is obtained by replacing the (first or second) equation in system A with the sum of that equation and (3, 9, -9, -3) times the (first or second) equation, is the same as the solution to system A.
To determine this, we can compare the solutions of system A and system B. If the solutions are the same, then the solution to system B is the same as the solution to system A. If the solutions are different, then the solution to system B is not the same as the solution to system A.
Let's work through an example to illustrate the process:
System A:
Equation 1: a + 2b = 5
Equation 2: 3a - 4b = 12
System B:
Equation 1: (a + 2b) + (3, 9, -9, -3)(a + 2b) = 5 + (3, 9, -9, -3) * 5
Equation 2: 3a - 4b = 12
We solve both systems and compare the solutions to determine if they are the same or not.
By solving system A, we find that a = 2 and b = 1. Therefore, the solution to system A is (2, 1).
By solving system B, we find that a = 2 and b = 1. Therefore, the solution to system B is also (2, 1).
Since the solutions to both systems are the same, we can conclude that the solution to system B is the same as the solution to system A.