Final answer:
To obtain System B from System A, we replace the second equation with a multiple of the other equation (Answer A). However, the two systems are not equivalent because the change in the second equation means they have different solutions (Answer B).
Step-by-step explanation:
Let's analyze System A and System B to answer the given questions:
System A:
4x + 16y = 12
x + 2y = -9
System B:
4x + 16y = 12
x + 4y = 3
1) To transform System A into System B, we can observe that the first equation of both systems is identical. The second equation has changed, so this suggests that we have altered one of the equations. In particular, we can notice that the x-coefficient in the second equation remains the same, but the y-coefficient has been multiplied by 2 (from 2y to 4y), and the constant term has been changed from -9 to 3. This indicates that we have replaced the second equation with a new equation, rather than modifying it with a multiple of itself or the other equation, meaning the correct answer is: A) Replace one equation with a multiple of the other equation.
2) Are System A and System B equivalent? No, because the change made to the second equation alters the set of solutions the system can have. The second equation in both systems, which dictates the relationship between x and y, is fundamentally different. This means that the solutions to the equations in Systems A and B are also likely to be different, thus the answer is B) No.