Question

Use the table to answer the question.
System A System B

7x+4y=−4

5x+8y=28



7x+4y=−4

?

Which of the following terms will make the systems equivalent?


(1 point)
Responses

−12x−12y=24

negative 12 x minus 12 y equals 24
−14x−8y=8
negative 14 x minus 8 y equals 8
12x+12y=24
12 x plus 12 y equals 24
−14x−8y=−8

Answer 1

To determine which equation will make System B equivalent to System A, we first need to manipulate the equation from System A to see what form it takes.

We have:

1. **System A**:
\[
7x + 4y = -4
\]

**We should check the second equation in System B to see how it relates to System A.**

2. **System B**:
\[
5x + 8y = 28
\]

Now we can manipulate the equation from System B to see if we can find a relationship to the first equation from System A.

We can put both equations in a similar standard form \(Ax + By = C\) to see if they're equivalent:

1. Multiply **System A** equation by a scalar if needed, to reach similar coefficients with **System B**.
2. Rearrange **System B** equation:
Multiply the first equation \(7x + 4y = -4\) by 2 to match the variables better.

Multiplying:
\[
2(7x + 4y) = 2(-4) \implies 14x + 8y = -8
\]

Now, we have:

- **Transformed System A**:
\[
14x + 8y = -8
\]

Now we look at all the given choices to find which is equal to \(14x + 8y = -8\) after suitable manipulation:

1. **Check the first option**:
\[
-12x - 12y = 24
\]
Rewriting this:
\[
12x + 12y = -24 \quad \text{(not equivalent)}
\]

2. **Check the second option**:
\[
-14x - 8y = 8
\]
Rewriting this:
Multiplying by \(-1\):
\[
14x + 8y = -8 \quad \text{(equivalent)}
\]

3. **Check the third option**:
\[
12x + 12y = 24
\]
(not equivalent)

4. **Check the fourth option**:
\[
-14x - 8y = -8
\]
Rewriting this:
Multiplying by \(-1\):
\[
14x + 8y = 8 \quad \text{(not equivalent)}
\]

The only choice that is equivalent or can be manipulated to match \[14x + 8y = -8\] is:

\[
\boxed{-14x - 8y = 8}
\]