Solving Simultaneous Equations Using Elimination Quick Check

Question

2 of 52 of 5 Items

Question
Use 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

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

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

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

−14x−8y=8
negative 14 x minus 8 y equals 8
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Answer 1

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