Solving Simultaneous Equations Using Elimination Quick Check

To determine which term will make System B equivalent to System A, we can manipulate the equations in System A.

The first equation in both systems is the same:

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

We need to transform the second equation of System B into a form that matches System A. The second equation of System A is:

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

We want to find a second equation in System B that corresponds to \( 5x + 8y = 28 \) after scaling or modification.

Notice that if we multiply the first equation \( 7x + 4y = -4 \) by 2, we get:

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

This means that the equation \( -14x - 8y = 8 \) (which is just the negative of the new equation we've found) is equivalent to our original system.

Thus, the term that would make the systems equivalent is:

**−14x−8y=8**

So the correct response is:

**−14x−8y=8**