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
2y=12
2 y equals 12
−x−y=−1

Answer 1

To create a true equivalent system for either System A or System B, we need to manipulate one of the equations without changing its solution set.

1. Let's look at the equation from System A:

   • The second equation in System A is \( x + y = 11 \).
   • If we multiply the entire equation by 2, we get: \[ 2x + 2y = 22 \] (This is not one of the options.)

2. For the options provided, we analyze each one:

   • Option 1: \( 2x + 2y = 12 \) (not equivalent, doesn't equal 22)
   • Option 2: \( -2x - 2y = -22 \) (equivalent to \( 2x + 2y = 22 \))
   • Option 3: \( 2y = 12 \) (equivalent to \( y = 6 \), but not an equivalent system with the existing equations)
   • Option 4: \( -x - y = -1 \) (equivalent to \( x + y = 1 \), not related to \( x + y = 11 \))

The correct answer which shows an equation that creates a true equivalent system is:

−2x−2y=−22

This is equivalent to the existing equation \( x + y = 11 \).