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

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
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Answer 1

To determine which equation would make System A and System B equivalent, we need to analyze the given equation in System A and understand what it means for the systems to be equivalent.

The given equation in System A is:

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

For two systems of equations to be equivalent, they must contain equations that represent the same set of solutions. One way to find an equivalent equation is to manipulate the initial equation (by multiplying it by a constant).

To find an equivalent equation, let’s consider the original equation:

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

If we multiply this entire equation by -2, we get:

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

Thus, we can see that:

\[ -14x - 8y = 8 \]

is indeed an equivalent equation to \( 7x + 4y = -4 \).

Now, we can check the responses given:

1. \( 12x + 12y = 24 \) - Not equivalent.
2. \( -14x - 8y = -8 \) - Not equivalent.
3. \( -12x - 12y = 24 \) - Not equivalent.
4. \( -14x - 8y = 8 \) - Equivalent.

The correct answer is:

−14x−8y=8