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 −x−y=−1 negative x minus y equals negative 1 −2x−2y=−22 negative 2 x minus 2 y equals negative 22 2y=12 2 y equals 12

Answer 1

To determine which equation creates a true equivalent system, we need to analyze the equations given for System A and System B.

For System A, we have:
1. \(-x + y = 1\)

For System B, we have:
1. \(x + y = 11\)
2. \(x + y = 11\) (which is redundant)

### Checking the Options:

1. **\(2x + 2y = 12\)**:
- This can be simplified by dividing by 2:
\[
x + y = 6
\]
- This is not equivalent to either of the original equations.

2. **\(-x - y = -1\)**:
- If we multiply through by -1, we find:
\[
x + y = 1
\]
- This is equivalent to the first equation of System A.

3. **\(-2x - 2y = -22\)**:
- If we simplify by dividing by -2:
\[
x + y = 11
\]
- This is equivalent to the second equation of System B.

4. **\(2y = 12\)**:
- If we simplify, we find:
\[
y = 6
\]
- This does not provide an equivalent system since it is only one variable.

### Conclusion:

Both \(-x - y = -1\) and \(-2x - 2y = -22\) can create equivalent systems, but the question requests the one equation that creates a true equivalent system.

Choosing between them, \(-x - y = -1\) corresponds directly with the equation from System A and helps relate to both systems.

Therefore, the best choice for the equation creating a true equivalent system is:

**\(-x - y = -1\)**