To create a true equivalent system for System B, we need an equation that is equivalent to \( x + y = 11 \).
Let's analyze the answer choices one by one:
A. \( 2x + 2y = 12 \)
We can simplify this equation by dividing both sides by 2: \[ x + y = 6 \] This is not equivalent to \( x + y = 11 \).
B. \( -x - y = -1 \)
We can rearrange this equation by multiplying both sides by -1: \[ x + y = 1 \] This is not equivalent to \( x + y = 11 \).
C. \( -2x - 2y = -22 \)
We can simplify this equation by dividing both sides by -2: \[ x + y = 11 \] This is equivalent to \( x + y = 11 \).
D. \( 2y = 12 \)
We can simplify this equation by dividing both sides by 2: \[ y = 6 \] This does not relate to the sum \( x + y = 11 \) as a whole.
Thus, the correct choice that creates a true equivalent system is:
C. \( -2x - 2y = -22 \).