Question

In order to solve the following system of equations by subtraction, which of the following could you do before subtracting the equations so that one variable will be eliminated when you subtract them?

4x-2y=7
3x-3y=15

A. Multiply the top equation by-3 and the bottom equation by 2
B. Multiply the top equation by 1/3
C. Multiply the top equation by 15 and the bottom equation by 7
D. Multiply the top equation by 3 and the bottom equation by 4.​

Answer 1

9514 1404 393

Answer:

D. Multiply the top equation by 3 and the bottom equation by 4.​

Explanation:

If you're using subtraction, you want the coefficients of one of the variables to be the same in both equations. If the variable you choose is x, then you need to multiply the top equation by the coefficient of x in the bottom equation (3), and the bottom equation by the coefficient of x in the to equation (4). Doing this will make both x-coefficients equal to 3×4 = 12. In short, ...

Multiply the top equation by 3 and the bottom equation by 4.​