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

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

2y=12
2 y equals 12

−2x−2y=−22

Answer 1

To create a true equivalent system, you can manipulate the existing equations in the system.

The given equations for System A are:

1. \(-x + y = 1\)
2. \(x + y = 11\)

We want to find an equation that is equivalent to these.

Let's analyze the provided options:

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

   • If we divide the original equation \(x + y = 11\) by 1, we find \(2(x + y) = 2(11)\), which gives us \(2x + 2y = 22\), so this does not match with \(2x + 2y = 12\).

2. \(-x - y = -1\):

   • If we take the first equation \(-x + y = 1\) and multiply both sides by -1, we get \(-x - y = -1\). This means this is an equivalent equation.

3. \(2y = 12\):

   • This would imply \(y = 6\), which doesn't match our systems' equations.

4. \(-2x - 2y = -22\):

   • This is just multiplying the equation \(x + y = 11\) by -2, which gives us \(-2(x+y) = -2(11)\) thus resulting in \(-2x - 2y = -22\), but it would not be an option since it does not match what we already have.

Thus, the only choice that creates a true equivalent system is \(-x - y = -1\).