Question

Given the following system of equations:

−4x + 8y = 16
2x + 4y = 8

What action was completed to create this new equivalent system of equations?

−2x + 4y = 8
2x + 4y = 8

A.Multiply the second equation, 2x + 4y = 8, by −1.
B.Multiply the first equation, −4x + 8y = 16, by −1.
C.Divide the second equation, 2x + 4y = 8, by 2.
D.Divide the first equation, −4x + 8y = 16, by 2.

Answer 1

D.Divide the first equation, −4x + 8y = 16, by 2.

Explanation:

−4x + 8y = 16

2x + 4y = 8

Take the first equation and divide it by 2

−4x/2 + 8y/2 = 16/2

-2x + 4y = 8

Answer 2

D.Divide the first equation, −4x + 8y = 16, by 2.

Explanation:

All you have to do is look at the effect of the proposed action on the constant on the right to tell which answer choices are incorrect.

• A: you would get -8 on the right. Neither equation has that.
• B: you would bet -16 on the right. Neither equation has that.
• C: you would get 4 on the right. Neither equation has that.
• D: you would get -2x +4y = 8, matching the first equation of the new system exactly.