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14 March, 14:55

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

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Answers (1)
  1. 14 March, 15:01
    0
    B. divide both sides of the bottom equation by 2

    Step-by-step 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.
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