Use the table to answer the question.

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

2y=12
2 y equals 12

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

−x−y=−1
negative x minus y equals negative 1

−2x−2y=−22

Answer 1

To create an equivalent system, we can manipulate the equations from System A or System B to match them in terms of the variables involved.

Given equations:

1. System A: \(-x + y = 1\)
2. System B: \(x + y = 11\) (repeated)

Now let's analyze the options provided:

1. \(2y = 12\): This can be simplified to \(y = 6\), which does not relate to the original equations.

2. \(2x + 2y = 12\): This can be derived by multiplying the entire second equation \(x + y = 11\) by 2, giving us \(2x + 2y = 22\), which is not equivalent to the 11 we needed.

3. \(-x - y = -1\): If we multiply the entire System A equation \(-x + y = 1\) by -1, we get \(x - y = -1\), which is not this option but shows a similar form.

4. \(-2x - 2y = -22\): This can be derived by multiplying \(x + y = 11\) by -2, giving us \(-2x - 2y = -22\), which is a true equivalent system based on the second equation.

Conclusion: The correct response that shows the equation that creates a true equivalent system is:

\(-2x - 2y = -22\).