Use the table to answer the question.

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 y equals 8

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

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

−12x−12y=24

Answer 1

To determine which of the given equations makes the systems equivalent, we need to manipulate one of the original equations.

The first equation in System A is: \[ 7x + 4y = -4 \]

The second equation in System B is: \[ 5x + 8y = 28 \]

To check if the proposed equations can be made equivalent, let’s manipulate the first equation, \( 7x + 4y = -4 \), by multiplying it by a constant.

Let's multiply the entire equation by -2: \[ -2(7x + 4y) = -2(-4) \] This gives: \[ -14x - 8y = 8 \]

Now let's compare this result with the choices given:

1. \(-14x - 8y = 8\)
2. \(-14x - 8y = -8\)
3. \(12x + 12y = 24\)
4. \(-12x - 12y = 24\)

From our transformation of the original equation, the correct term that makes the systems equivalent is: \[ -14x - 8y = 8 \]

Therefore, the answer is: −14x−8y=8 (negative 14 x minus 8 y equals 8).