Question

Which of the following steps would you perform to the system of equations below so that the equations have opposite y-coefficients?

4x +2y=4
12x + y=22


A. divide both sides of the top equation by 3
B. divide both sides of the bottom equation by 2
C. multiply both sides of the bottom equation by 3
B. multiply both sides of the top equation by 3

Answer 1

B. divide both sides of the bottom equation by 2

Explanation

If opposite means additive inverse, then none of the answers is correct

The given system of equations is

4x+2y=4

12x+y=22

The coefficient of y in the top equation is 2 and the coefficient of y in the bottom equation is 1.

One way to make the coefficient of y have opposite sign is to multiply the bottom equation by -2 to get:

4x+2y=4

-24x-2y=-44

Or we divide the top equation by -2

-2x-y=-2

12x+y=22

If opposite means, multiplicative inverse, then dividing through both sides of the bottom equation by 2 gives:

4x +2y=4

6x + ½y=11

Hence the second choice is correct.