Use the table to answer the question.

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

2y=12
2 y equals 12

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

2x+2y=12
2 x plus 2 y equals 12
Skip to navigation

page 15 of 15

Answer 1

To determine which equation creates a true equivalent system with the given systems, we need to see if any of the options are equivalent to the original equations in system A or system B.

The equations in System A are:

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

The second equation \(x + y = 11\) is also given in System B.

Next, let's check each option to see if it maintains the same solutions as the above equations:

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

   • Dividing by -2 gives: \(x + y = 11\) (which is equivalent to one of our equations).

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

   • Dividing the whole equation by 2 gives: \(y = 6\). This is not equivalent to any of the original equations.

3. Option: \(-x - y = -1\)

   • Rearranging gives: \(x + y = 1\) (which is not equivalent to any of the original equations).

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

   • Dividing by 2 gives: \(x + y = 6\) (which is not equivalent to any of the original equations).

The only option that is equivalent to the original equations is:

Option: (-2x - 2y = -22

So the correct answer is:

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

Answer 2

Use the table to answer the question.

System A
7x+4y=−4

5x+8y=28
System B
7x+4y=−4

?

Which of the following terms will make the systems equivalent?


(1 point)
Responses

12x+12y=24
12 x plus 12 y equals 24

−14x−8y=−8
negative 14 x minus 8 equals negative 8

−12x−12y=24
negative 12 x minus 12 y equals 24

−14x−8y=8
negative 14 x minus 8 y equals 8
Skip to navigation

Answer 3

To determine which option will make the systems equivalent, we need to check if any of the choices can be manipulated to match the second equation of System A, which is:

1. \(7x + 4y = -4\)
2. \(5x + 8y = 28\)

System B begins with the same first equation as System A:

1. \(7x + 4y = -4\)

We are looking for an equation that is equivalent to the second equation of System A: \(5x + 8y = 28\).

Let's analyze each option:

1. Option: \(12x + 12y = 24\)

   • This can be simplified by dividing everything by 12, giving us \(x + y = 2\), which is not equivalent to \(5x + 8y = 28\).

2. Option: \(-14x - 8y = -8\)

   • Dividing everything by -2 gives \(7x + 4y = 4\), which does not match \(5x + 8y = 28\).

3. Option: \(-12x - 12y = 24\)

   • Dividing everything by -12 gives \(x + y = -2\), which is not equivalent to \(5x + 8y = 28\).

4. Option: \(-14x - 8y = 8\)

   • Dividing everything by -2 gives \(7x + 4y = -4\) (which is our first equation in both systems) and does not appear to match \(5x + 8y = 28\).

None of these options seem to create a connection with \(5x + 8y = 28\) directly. However, let's try to manipulate one of the options to see if they can be equivalent.

Now let’s check if any of these attempts reveal a path to find a match:

Conclusion:

Since none of the choices appear to produce the second equation \(5x + 8y = 28\) directly or indirectly, it seems that options given do not provide a correct matching equation for the second system of equations.

Based on this analysis, none of the provided options create a true equivalent system in combination with the existing equations. Hence, it would imply that there might be a different or error in available options provided. If you can provide a check against another question matrix or equations, it would be helpful to refine these further.