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

2y=12
2 y equals 12

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

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

2x+2y=12

Answer 1

To create a true equivalent system for System A and System B, we can modify the equations while maintaining their solutions.

Let's start with the given equation from System A:

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

We can manipulate this equation:

• Multiply the entire equation by \(-1\): \[x - y = -1\]

Now let's look at the options provided:

1. \(2y = 12\) (this simplifies to \(y = 6\))
2. \(-x - y = -1\) (this is equivalent to \(x + y = 1\))
3. \(-2x - 2y = -22\) (this simplifies to \(2x + 2y = 22\))
4. \(2x + 2y = 12\) (this simplifies to \(x + y = 6\))

None of these options directly provide an equivalent form of \(-x + y = 1\). However, let’s analyze option 3, which is \(-2x - 2y = -22\).

If we divide this equation by -2, we get:

\[ x + y = 11 \]

This is indeed equivalent to the given equation from System B.

So the correct answer is:

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