Ask a New Question
Menu

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=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

1 answer

To find an equation that creates a true equivalent system to the given systems, we need to analyze the provided equations.

The two equations given from System A and System B are:

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

Now, eliminate \(y\) from these equations to find an equivalent one.

First, we can manipulate these equations:

  1. Rearranging the first equation: \(y = x + 1\)

  2. Substitute \(y\) in the second equation: \[ x + (x + 1) = 11 \] \[ 2x + 1 = 11 \] \[ 2x = 10 \] \[ x = 5 \] Now substitute \(x\) back to find \(y\): \[ y = 5 + 1 = 6 \]

Thus, one solution is \(x = 5\) and \(y = 6\).

Next, let's check which of the given responses corresponds to the original equations and gives the same solutions.

To determine if the proposed equations are equivalent:

  1. \(2x + 2y = 12\) - Divide by 2: \[ x + y = 6 \quad \text{(not equivalent)} \]

  2. \(2y = 12\) - Divide by 2: \[ y = 6 \quad \text{(not equivalent to the original)} \]

  3. \(-2x - 2y = -22\) - Divide by -2: \[ x + y = 11 \quad \text{(this is equivalent to System B)} \]

  4. \(-x - y = -1\) - Multiply by -1: \[ x + y = 1 \quad \text{(not equivalent)} \]

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

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