Use the table to answer the question.

Question

System A
−x+y=1

x+y=11

System B
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

2y=12
2 y equals 12

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

−x−y=−1

Answer 1

To create a true equivalent system with System B, we need to look at the existing equations.

The equation \( x + y = 11 \) is already in System B.

Now let's analyze which of the options could create an equivalent system when combining it with \( x + y = 11 \).

1. Option 1: \( 2x + 2y = 12 \)

   This equation can be simplified by dividing all terms by 2: \[ x + y = 6 \] This is not equivalent to \( x + y = 11 \).

2. Option 2: \( 2y = 12 \)

   This can be simplified to: \[ y = 6 \] This provides a fixed value for \( y \) but does not create an equivalent system.

3. Option 3: \( -2x - 2y = -22 \)

   Simplifying this yields: \[ x + y = 11 \] This is equivalent to the known equation in System B and thus works.

4. Option 4: \( -x - y = -1 \)

   This simplifies to: \[ x + y = 1 \] This is not equivalent to \( x + y = 11 \).

From the options given, the equation that creates a true equivalent system is:

−2x−2y=−22.