Question

Use the table to answer the question.

System A
−x+y=1

x+y=11

System B
x+y=11

?

Which of the following shows the equation that creates a true equivalent system?

(1 point)
Responses

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

2y=12
2 y equals 12

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

−x−y=−1

Answer 1

To create a true equivalent system with System B, we need to look at the existing equations.

The equation \( x + y = 11 \) is already in System B.

Now let's analyze which of the options could create an equivalent system when combining it with \( x + y = 11 \).

1. **Option 1: \( 2x + 2y = 12 \)**

This equation can be simplified by dividing all terms by 2:
\[
x + y = 6
\]
This is not equivalent to \( x + y = 11 \).

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

This can be simplified to:
\[
y = 6
\]
This provides a fixed value for \( y \) but does not create an equivalent system.

3. **Option 3: \( -2x - 2y = -22 \)**

Simplifying this yields:
\[
x + y = 11
\]
This is equivalent to the known equation in System B and thus works.

4. **Option 4: \( -x - y = -1 \)**

This simplifies to:
\[
x + y = 1
\]
This is not equivalent to \( x + y = 11 \).

From the options given, the equation that creates a true equivalent system is:

**−2x−2y=−22**.