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Question To solve this system, you could do the following steps: 3x+4y=48 6x+2y=60 (6 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. 1. Choose the best method to solve by looking at the way the equations are set up for you: Response area 2. Using the best method, how could you get the x variables to cancel out? Response area 3. After you complete step 2, what would your top equation be? Response area 4. Line them up and add the equations together to get this equation. Response area 5. Solve for y. Response area 6. Solve for x. Response area

1 answer

Let's go through the steps to solve the system of equations:

Given Equations:

  1. \( 3x + 4y = 48 \) (Equation 1)
  2. \( 6x + 2y = 60 \) (Equation 2)

Step 1: Choose the best method

Response area: Elimination method

Step 2: How could you get the x variables to cancel out?

To use the elimination method, we can multiply Equation 1 by 2 to get the coefficients of \( x \) to match:

  • Multiply Equation 1 by 2: \[ 2(3x + 4y) = 2(48) \Rightarrow 6x + 8y = 96 \quad (Equation 3) \]

Response area: Multiply the first equation by 2.

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

The top equation after multiplying will be: Response area: 6x + 8y = 96

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

We align both modified equations:

  • New Equation: \( 6x + 8y = 96 \) (Equation 3)
  • Existing Equation: \( 6x + 2y = 60 \) (Equation 2)

Now we can subtract Equation 2 from Equation 3 to eliminate \( x \): \[ (6x + 8y) - (6x + 2y) = 96 - 60 \] This simplifies to: \[ 6y = 36 \]

Response area: 6y = 36

Step 5: Solve for y.

To solve for \( y \): \[ y = \frac{36}{6} = 6 \]

Response area: y = 6

Step 6: Solve for x.

Now that we have \( y \), we can substitute it back into one of the original equations to solve for \( x \). We'll use Equation 1: \[ 3x + 4(6) = 48 \] This simplifies to: \[ 3x + 24 = 48 \] Now, subtract 24 from both sides: \[ 3x = 48 - 24 \] \[ 3x = 24 \] Dividing both sides by 3 gives: \[ x = \frac{24}{3} = 8 \]

Response area: x = 8

Final Answer Summary:

  • x = 8
  • y = 6