Question

Use the table to answer the question.

System A System B
−x+y=1


x+y=11


x+y=11


?


Which of the following shows the equation that creates a true equivalent system?

(1 point)
Responses

2x+2y=12
2 x plus 2 y equals 12

−2x−2y=−22
negative 2 x minus 2 y equals negative 22

2y=12
2 y equals 12

−x−y=−1

Answer 1

To find an equivalent system of equations for System A and System B, we need to determine which of the given options maintains the same relationship as the original equations.

Let's analyze the equations:

1. The first equation from System A is \(-x + y = 1\).
2. The two equations from System B are \(x + y = 11\) (repeated).

To create an equivalent equation, we can manipulate the existing equations in System A or B.

Starting with \(x + y = 11\):
- We can multiply the entire equation by 2 to yield:
\[
2x + 2y = 22
\]

However, notice this is not one of the options provided. Therefore, let's confirm the validity of each of the provided response options.

### Evaluating each option:
1. **\(2x + 2y = 12\)**:
- Divide by 2: \(x + y = 6\) (not equivalent to \(x + y = 11\)).

2. **\(-2x - 2y = -22\)**:
- Divide by -2: \(x + y = 11\) (this is equivalent to one of the equations in System B).

3. **\(2y = 12\)**:
- Divide by 2: \(y = 6\) (not equivalent to either equation).

4. **\(-x - y = -1\)**:
- Rearranging gives \(x + y = 1\) (not equivalent to \(x + y = 11\)).

### Conclusion:
The correct response that shows an equation that creates a true equivalent system is:
**\(-2x - 2y = -22\)**.