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

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

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

12x+12y=24

Answer 1

To determine which of the provided options will make the systems equivalent, we can start by analyzing one of the equations in the system. We already have the equation from System A:

\[ 7x + 4y = -4 \]

We know that two equations are equivalent if they represent the same line, which can be achieved by multiplying the entire equation by a non-zero constant.

Let's multiply the first equation by -2 to find an equivalent equation:

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

Now we can compare this result with the options given:

1. −14x−8y=8 (this matches what we found)
2. −12x−12y=24 (this does not match)
3. −14x−8y=−8 (this does not match)
4. 12x+12y=24 (this does not match)

Therefore, the term that will make the systems equivalent is:

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