Question

Which of these strategies would eliminate a variable in the system of equations?

Answer 1

Multiply the top equation by 6 and and the bottom equation by –5 and then add the equations is the correct answer.

Solution:

Given system of equations:

8x + 5y = –7 – – – – (1)

–7x + 6y = –4 – – – – (2)

Multiply top equation by 6 and and bottom equation by –5

(1) × 6 ⇒ 48x + 30y = –42

(2) × –5 ⇒ 35x – 30y = 20

Now add these two equations, we get

(48x + 30y) + (35x – 30y) = –42 + 20

48x + 35x + 30y  – 30y = –42 + 20

83x = –20

The variable y is eliminated.

Therefore Multiply the top equation by 6 and and the bottom equation by –5 and then add the equations is the correct answer.