To determine which equation creates a true equivalent system for System B, we need to analyze the equations given in the table.
From System B, we have the equation:
\[ x + y = 11 \]
To create an equivalent system, we can manipulate this equation.
-
Multiply the entire equation by 2: \[ 2(x + y) = 2(11) \implies 2x + 2y = 22 \]
-
Multiply the entire equation by -2: \[ -2(x + y) = -2(11) \implies -2x - 2y = -22 \]
-
Rearranging the original equation: \[ x + y - 11 = 0 \implies -x - y = -11 \]
-
Isolate \(y\): \[ y = 11 - x \] This does not yield a standard system equivalent.
Now, let's examine the response options given:
- 2x + 2y = 12 - This is not equivalent to \(x + y = 11\).
- −2x − 2y = −22 - This is equivalent to \(x + y = 11\) when divided by -2.
- −x − y = −1 - This is not equivalent to \(x + y = 11\).
- 2y = 12 - This simplifies to \(y = 6\) and does not represent the same relationship.
The correct answer is: −2x−2y=−22.