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

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.