Question

Solving Simultaneous Equations Using Elimination Quick Check
1 of 51 of 5 Items
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

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

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

2y=12
2 y equals 12

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

To find the equation that creates a true equivalent system to the given systems, we can manipulate one of the original equations. Here we have:

For System A:
\[
-x + y = 1
\]

For System B (which has the same equation):
\[
x + y = 11
\]

An equivalent system can be derived by multiplying the entire equation by a constant.

1. Let's multiply the first equation \(-x + y = 1\) by -2 to create an equivalent equation:

\[
-2(-x + y) = -2(1)
\]
This simplifies to:
\[
2x - 2y = -2
\]

2. Rearranging gives:
\[
2x - 2y + 2 = 0
\]
This is equivalent to:
\[
2x - 2y = -2
\]

This is similar to the option provided; however, we need to further analyze the given options:
- **−2x−2y=−22**: This is not equivalent since it is not consistent with the multiplier used.
- **2x+2y=12**: Not equivalent.
- **2y=12**: Not equivalent.
- **−x−y=−1**: This is just a rearrangement of the original equation \(-x + y = 1\).

None of these options give us the exact manipulation needed.

However, if we focus and summarize which option might relate closely to the transformations:
**The equation -x - y = -1 is indeed equivalent to the first equation multiplied by -1.**

Thus, the most suitable choice would be:

**−x−y=−1**