Question

se 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

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

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

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

12x+12y=24

Answer 1

To determine which of the options will make the systems equivalent, we need to analyze the given equations.

You are provided with:

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

System B:
2. \( 5x + 8y = 28 \)

To check for equivalence, we need to manipulate the first equation in some way to make it look like the second.

### Option 1: \(-14x - 8y = -8\)
To see if this is equivalent, let's rewrite the first equation:
- Multiply \( 7x + 4y = -4 \) by \(-2\):
\[
-2(7x + 4y) = -2(-4)
\]
This results in:
\[
-14x - 8y = 8
\]
This is not equal to \(-14x - 8y = -8\).

### Option 2: \(-14x - 8y = 8\)
From our earlier operation, after multiplying the first equation by -2, we have:
\(-14x - 8y = 8\),
which we derived from the first equation.
So, this makes the systems equivalent.

### Option 3: \(-12x - 12y = 24\)
We will manipulate the first equation too:
- Multiply \( 7x + 4y = -4 \) by \(-\frac{12}{7}\) to compare:
\[
-\frac{12}{7}(7x + 4y) = -\frac{12}{7}(-4)
\]
This doesn't transform it into the format of the other options. Thus, it is not equivalent.

### Option 4: \(12x + 12y = 24\)
This does not match either equation, so it cannot represent an equivalent system.

### Conclusion:
The correct option that makes the systems equivalent is:
**−14x−8y=8**.