Question

Use the table to answer the 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

2x+2y=12
2 x plus 2 y equals 12

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

−2x−2y=−22

Answer 1

To create a true equivalent system from the equations provided in System A and System B, we need to find an equation that maintains the same solutions as the original equations.

The equations in System B, \(x + y = 11\), can be manipulated.

If we multiply both sides of the equation by 2, we would have:
\[
2(x + y) = 2(11)
\]
This simplifies to:
\[
2x + 2y = 22
\]
Now, to check which option matches or creates an equivalent system, let’s look at the options:

1. \(2y = 12\) – This simplifies to \(y = 6\), not equivalent to the original.
2. \(2x + 2y = 12\) – This is not equivalent to the original \(x + y = 11\).
3. \(-x - y = -1\) – This can also be transformed by multiplying by -1 to get \(x + y = 1\), which is not equivalent to \(x + y = 11\).
4. \(-2x - 2y = -22\) – This is equivalent to dividing by -2, which gives us \(x + y = 11\).

Therefore, the equation that creates a true equivalent system is:
\[
-2x - 2y = -22
\]

Thus, the correct answer is:

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