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

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

2y=12

Answer 1

To create an equivalent system, we can manipulate the existing equations in System B to see which option maintains their equivalence. The equations present in System B are:

- \( x + y = 11 \)

Now, let’s consider the options one by one:

1. **\( 2x + 2y = 12 \)**:
- To check if it's equivalent, we can divide the entire equation by 2:
- \( x + y = 6 \)
- This is **not** equivalent to \( x + y = 11 \).

2. **\( -2x - 2y = -22 \)**:
- Dividing the entire equation by -2 gives:
- \( x + y = 11 \)
- This is equivalent to \( x + y = 11 \).

3. **\( -x - y = -1 \)**:
- To check equivalence, we can multiply the equation by -1 to get:
- \( x + y = 1 \)
- This is also **not** equivalent to \( x + y = 11 \).

4. **\( 2y = 12 \)**:
- Dividing the entire equation by 2 gives:
- \( y = 6 \)
- This does not relate directly to \( x + y = 11 \) in an equivalent way.

The only option that results in an equivalent equation to \( x + y = 11 \) is:

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

So, the answer is:

**−2x−2y=−22**.