Question

Renee wants to solve the system of equations. Which number can she multiply the first equation by so that when the two equations are added together, the y term is eliminated?
Two-thirds x + one-fifth y = 6

One-sixth x minus 3 y = 8

A.-15
B.-5
C.5
D.15

Answer 1

Answer:

eliminate D

Step-by-step explanation:

Answer 2

Answer:

Multiply the first equation by 15 (Answer D)

Step-by-step explanation:

Writing these equations symbolically, we have:

(2/3)x + (1/5)y = 6

(1/6)x - 3y = 8

Which number can she multiply the first equation by so that when the two equations are added together, the y term is eliminated?  After this multiplication, we should have +3y in the first equation; then 3y - 3y = 0 as desired.  The coefficient of the y term in the first equation is (1/5), whereas we want it to be +3.  

Multiplying the first equation by 15, we get 10x + 3y = 90.

Then our system is:

10x + 3y = 90

(1/6)x - 3y = 8

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(61/6)x = 98    (the variable y has been temporarily eliminated).