Use the table to answer the question.

Question

System A System B
−x+y=1
−
x
+
y
=
1

x+y=11
x
+
y
=
11

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

2y=12
2
y
=
12
2 y equals 12

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

2x+2y=12

Answer 1

To determine which equation creates a true equivalent system, we first need to look at the existing equations in the systems provided.

The equations for both systems are:

System A:

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

System B:

1. \( x + y = 11 \) (repeated, so it doesn't provide new information)

To identify an equivalent system, we can manipulate one of the existing equations. An equation is equivalent if it represents the same line or value on a graph.

Checking the Options

1. \(-2x - 2y = -22\): If we divide this equation by -2, we would get \(x + y = 11\), which is equivalent to one of the equations in System B.

2. \(2y = 12\): If you solve for \(y\), you get \(y = 6\). This does not create an equivalent system as it doesn't relate to the original equations effectively.

3. \(-x - y = -1\): If we rearrange this equation, we can adjust it to \(x + y = 1\), which is not equivalent to \(x + y = 11\).

4. \(2x + 2y = 12\): If we divide this equation by 2, we arrive at the equation \(x + y = 6\), which is also not equivalent to the equations in the original systems.

Conclusion

The only equation that forms a true equivalent system is:

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

This represents the same relationship as \(x + y = 11\) and thus creates a valid equivalent system.