Select the correct answer.

Question

A system of equations and its solution are given below.

System A

Choose the correct option that explains what steps were followed to obtain the system of equations below.

System B

A.
To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by 5. The solution to system B will be the same as the solution to system A.
B.
To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by 3. The solution to system B will be the same as the solution to system A.
C.
To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -6. The solution to system B will not be the same as the solution to system A.
D.
To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -5. The solution to system B will not be the same as the solution to system A.

Answer 1

To determine the correct option, we need to analyze the transformation from System A to System B. This generally involves looking at how the equations have been modified and whether the operations performed preserve the solutions.

The key rules of manipulating systems of equations state that:

1. You can add or subtract equations to form new equations.
2. You can multiply an entire equation by a non-zero constant.

These operations maintain the solution to the system, provided they are executed correctly.

Without specific equations from System A and System B, and based on the options given, I can analyze the descriptions:

• Option A talks about replacing the second equation with a sum involving the first equation multiplied by 5. If this operation is valid, the solutions should remain the same.
• Option B involves a multiplication by 3, which would also maintain the solution.
• Option C involves a multiplication by -6, which could potentially change the solution depending on the equations themselves.
• Option D mentions multiplying by -5; this also can maintain equivalence if performed correctly.

If specific equations were provided, we would evaluate by substituting the manipulated equation into the context of the system to see if they yield the same solutions.

Given the lack of specific equations, without loss of generality, the most accurate selection is dependent on the manipulations described.

If you can provide the actual equations from System A and System B, I can help you confirm the correct option directly. However, based on just the explanations provided, the options A and B suggest that the solutions remain the same, while options C and D imply they do not.

Thus, based on that reasoning, if the operations described in A or B were appropriately implemented without contradicting any fundamental rules of algebra, either A or B could be considered correct. However, if the transformations suggested in C and D are valid but change the solutions, they would be correct in that specific context as well.

In the absence of further information, I cannot explicitly choose one of the options as definitively correct. More information on System A and System B is needed to make a conclusive determination.