Question

by graphing how could you get the x variables to cancel out?

3x+4y=48
6x+2y=60

Answer 1

To cancel out the x variables, you need to multiply one of the equations by a certain number so that when you add or subtract the two equations, the coefficients of x will cancel out.

Looking at the given equations:
3x + 4y = 48 ...(1)
6x + 2y = 60 ...(2)

Let's multiply equation (1) by -2 and equation (2) by 3 so that the coefficients of x are opposites of each other:
-2(3x + 4y) = -2(48)
3(6x + 2y) = 3(60)

This yields:
-6x - 8y = -96 ...(3)
18x + 6y = 180 ...(4)

Now, when you add equations (3) and (4), the x variables will cancel out:
(-6x - 8y) + (18x + 6y) = (-96) + 180

This simplifies to:
12y = 84

Thus, by adding equations (3) and (4), you can cancel out the x variables.