Question

Using substitution how could you get the x variables to cancel out?
3x+4y=48 and 6x+2y=60
A. Multiply the bottom equation x 2
B. Multiply the top equation x -2

Answer 1

To get the x variables to cancel out, you need to make the coefficients of x in both equations the same or opposite.

In this case, the coefficients of x in the first equation are 3 and in the second equation are 6. To make them the same, you could multiply the top equation by 2 (option A) or the bottom equation by -2 (option B).

If you multiply the top equation by 2, you get:

2(3x + 4y) = 2(48)
6x + 8y = 96

If you multiply the bottom equation by -2, you get:

-2(6x + 2y) = -2(60)
-12x - 4y = -120

In both cases, the coefficients of x are the same (6 and -12), allowing you to cancel out the x variables when you subtract these two equations.