Question

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

1. Choose the best method to solve by looking at the way the equations are set up for you:
graphing, elimination, substitution

2. Using the best method, how could you get the x variables to cancel out? Divide the bottom equation by 2.
Divide the top equation by 4, Multiply the top equation x -2 Multiply the bottom equation x -2.

3. After you complete step 2, what would your top equation be?
x+2y=46, -6x+4y=96, -6x-8y=-96, 3x+y=30
4. Line them up and add the equations together to get: -6=-36, 8y=96, 6y=-96, -8y=-96
5. Solve for y.
6. Solve for x.

Answer 1

To solve the system of equations, we will use the elimination method. We will start by multiplying the top equation by 2 and the bottom equation by 4 to cancel out the x variables.

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

4*(6x + 2y) = 4*60
24x + 8y = 240

Now, we can subtract the second equation from the first equation to eliminate the x variable:

(6x + 8y) - (24x + 8y) = 96 - 240
-18x = -144
x = (-144) / (-18)
x = 8

Next, we substitute the value of x into one of the original equations to solve for y. We will use the first equation:

3x + 4y = 48
3*8 + 4y = 48
24 + 4y = 48
4y = 48 - 24
4y = 24
y = 24 / 4
y = 6

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