Question

Which of the following shows the equation that creates a true equivalent system? (1 point)

Table:

System A System B
-x + y = 1 x + y = 11
x + y = 11 ?


Answers:

-2x - 2y = -22
-x - y = -1
2y = 12
2x + 2y = 12

Answer 1

To create a true equivalent system for System B, we need to find an equation that, when simplified or manipulated, is consistent with the equations in System A.

Let's analyze the System A equations:

1. From the first equation in System A:
\(-x + y = 1\)

Rearranging this gives:
\[y = x + 1\]

2. From the second equation in System A:
\[x + y = 11\]
Here, we can express \(y\) in terms of \(x\):
\[y = 11 - x\]

Setting the two expressions for \(y\) equal to each other from both equations:
\[
x + 1 = 11 - x
\]
Solving for \(x\):
\[
2x = 10 \implies x = 5
\]
Substituting \(x = 5\) back into one of the equations to find \(y\):
\[
y = 5 + 1 = 6
\]

So, the solution of System A is \( (5, 6) \).

Now let's check the given equations to see which one fits System B:

1. **Option 1**: \(-2x - 2y = -22\)

Dividing the entire equation by -2 gives:
\[x + y = 11\] (which is the second equation in System B).

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

Rearranging gives:
\[x + y = 1\] (which doesn't match any equation in System B).

3. **Option 3**: \(2y = 12\)

Dividing by 2 gives:
\[y = 6\]
This does not include \(x\) and is not equivalent to either equation in System B.

4. **Option 4**: \(2x + 2y = 12\)

Dividing the entire equation by 2 gives:
\[x + y = 6\] (which also doesn't match either equation in System B).

From this analysis, the only option that produces an equivalent system is:

**Answer: -2x - 2y = -22**.