The equations - a - 7b = 14 and - 4a - 14b = 28 represent a system of linear equations. Which statement correctly explains how to eliminate the variable b when solving the system of equations?

A. Multiply the first equation by - 2 and add it to the second equation. Then solve the resulting equation, - 2a = 0.

B. Multiply the first equation by 2 and add it to the second equation. Then solve the resulting equation, - 2a = 0.

C. Divide the second equation by - 4 and add it to the first equation.

D. Divide the second equation by 4 and add it to the first equation.

Question

Mathematics

Deangelo

10 June, 21:22

The equations - a - 7b = 14 and - 4a - 14b = 28 represent a system of linear equations. Which statement correctly explains how to eliminate the variable b when solving the system of equations?

A. Multiply the first equation by - 2 and add it to the second equation. Then solve the resulting equation, - 2a = 0.

B. Multiply the first equation by 2 and add it to the second equation. Then solve the resulting equation, - 2a = 0.

C. Divide the second equation by - 4 and add it to the first equation.

D. Divide the second equation by 4 and add it to the first equation.

+4

Answers (2)

Know the Answer?

Aryana Guerra · Answer 1

-7 times - 2=14

14-14=0

multily the first equaton by - 2 and add it to the second equation

result is - 2a=0

A is answer

Hadassah Mcintyre · Answer 2

In order to eliminate the variable b via addition of the two equations, we must first make the coefficients of b in the two equations the same but with opposite signs. Thus, when we multiply the first equation by - 2,

-2 (-a - 7b = 14)

= 2a + 14b = - 28

The coefficients of b in both equations are now equal with opposite signs. We now add,

2a - 4a + 14b - 14b = 28 - 28

= - 2a = 0

The answer is A.