Question

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

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:

2. Using the best method, how could you get the x variables to cancel out?

3. After you complete step 2, what would your top equation be?

4. Line them up and add the equations together to get this equation.

5. Solve for y.

6. Solve for x.

Answer 1

To solve the system of equations:

1. Choose the best method to solve by looking at the way the equations are set up for you:
- The equations are easy to manipulate, so the elimination method (also known as the addition method) is a good choice since it allows for straightforward cancellation of one of the variables.

2. Using the best method, how could you get the x variables to cancel out?
- To eliminate \( x \), we need to make the coefficients of \( x \) in both equations equal. We can multiply the first equation by 2, which will transform \( 3x \) into \( 6x \), matching the coefficient of \( x \) in the second equation.

3. After you complete step 2, what would your top equation be?
- The first equation, \( 3x + 4y = 48 \), multiplied by 2 becomes:
\[
6x + 8y = 96
\]

4. Line them up and add the equations together to get this equation.
- Now we have:
\[
6x + 8y = 96 \quad \text{(new first equation)}
\]
\[
6x + 2y = 60 \quad \text{(second equation)}
\]
- Next, we will subtract the second equation from the new first equation:
\[
(6x + 8y) - (6x + 2y) = 96 - 60
\]
- This simplifies to:
\[
6y = 36
\]

5. Solve for y.
- Divide both sides by 6:
\[
y = 6
\]

6. Solve for x.
- Now substitute \( y = 6 \) back into one of the original equations. We'll use the second equation \( 6x + 2y = 60 \):
\[
6x + 2(6) = 60
\]
\[
6x + 12 = 60
\]
\[
6x = 60 - 12
\]
\[
6x = 48
\]
\[
x = 8
\]

The solution to the system of equations is:
\[
x = 8, \quad y = 6
\]