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

2y=12
2 y equals 12

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

2x+2y=12

Answer 1

To find an equation that creates a true equivalent system, we need to work with the equations provided in System A and System B.

Starting with System A:
1. \(-x + y = 1\)

And from System B, we have:
1. \(x + y = 11\) (which appears twice).

To create equivalent systems, we will manipulate the first equation from System A.

### Check the options given:

1. **−2x−2y=−22**:
This can be derived from \(-x + y = 1\) by first multiplying the entire equation by 2:
\[
-2(-x + y) = 2(1) \implies -2x + 2y = 2
\]
However, this does not correspond to a direct equivalent transformation, and can be dismissed as valid for this context.

2. **2y=12**:
This can be derived by manipulating the second equation from System B:
\[
x + y = 11 \implies y = 11 - x
\]
There is no direct multiplication that can convert the equations in either system to this form.

3. **−x−y=−1**:
This can be derived by multiplying the equation from System A by 1 (which keeps it equivalent):
\[
-x + y = 1 \implies -1(x + y) = -1 \implies -x - y = -1
\]
This is indeed equivalent; however, it does not provide a system with the second equation in System B.

4. **2x+2y=12**:
This is derived by multiplying the second equation from System B \(x + y = 11\) by 2:
\[
2(x + y) = 2(11) \implies 2x + 2y = 22
\]
This is also not consistent with the systems provided.

### Conclusion

The equation that creates a true equivalent system based on the manipulations of the equations provided is:

**−x−y=−1**

Thus, the answer is:

**−x−y=−1**