Question

System A:
7x+4y=-4
5x+8y=28

System B:
7x+4y=-4
?

Which of the following terms will make the systems equivalent?

a. -14x-8y=8
b. 12x+12y=24
c. -12x-12y=24
d. -14x-8y=-8

Answer 1

but you have to pick one

Answer 2

To determine which term will make the systems A and B equivalent, we need to find the missing equation in System B.

Looking at System A:
7x + 4y = -4 ...(1)
5x + 8y = 28 ...(2)

We can see that to go from Equation (1) to Equation (2), we multiplied both sides of Equation (1) by 5 and Equation (2) by 2. Let's use this information to find the missing equation in System B.

If we multiply Equation (1) by 5, we get:
35x + 20y = -20

If we multiply Equation (2) by 2, we get:
10x + 16y = 56

So, the missing equation in System B is:
35x + 20y = -20.

Comparing this with the given options:
a. -14x - 8y = 8
b. 12x + 12y = 24
c. -12x - 12y = 24
d. -14x - 8y = -8

We can see that none of the given options match the missing equation in System B. Therefore, none of the options will make the systems A and B equivalent.

Answer 3

Apologies for the confusion. In that case, based on the given options, the closest match to the missing equation in System B, which is 35x + 20y = -20, would be option d. -14x - 8y = -8.