Question

To solve this system, you could do the following steps:

3x+4y=48

6x+2y=60
Choose the best method to solve by looking at the way the equations are set up for you:
Using the best method, how could you get the x variables to cancel out?
. After you complete step 2, what would your top equation be? Response area
Line them up and add the equations together to get this equation.
. Solve for y.

. Solve for x.

Answer 1

One possible method to solve this system of equations is to use the method of substitution.

To cancel out the x variables, we can multiply the first equation by 2 and the second equation by -3:

2(3x+4y) = 2(48)
-3(6x+2y) = -3(60)

This gives us:

6x + 8y = 96
-18x - 6y = -180

Now, we can line up the equations and add them together:

(6x + 8y) + (-18x - 6y) = 96 + (-180)

Simplifying this equation gives us:

-12x + 2y = -84

We can solve for y by isolating it on one side of the equation:

2y = -84 + 12x
y = -42 + 6x

Now that we have the equation for y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:

3x + 4(-42 + 6x) = 48

Simplifying this equation gives us:

3x - 168 + 24x = 48
27x - 168 = 48
27x = 216
x = 8

Now that we have the value of x, we can substitute it back into the equation for y:

y = -42 + 6(8)
y = -42 + 48
y = 6

Therefore, the solution to the system of equations is x = 8 and y = 6.