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

3x+4y=48

6x+2y=60

(6 points)
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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

Choose a method
Operation to get the x variables to cancel
Simplified top equation
After adding the equations
Solve for x and y
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1 answer

To solve the given system of equations, I'll guide you through the steps:

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

    • Elimination method (This method simplifies the calculations since the coefficients of \( y \) can be worked with easily).

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

    • Multiply the first equation by 2, so that the coefficients in front of \( x \) will be the same in both equations.

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

    • \( 6x + 8y = 96 \)

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

    • \( (6x + 8y) + (6x + 2y) = 96 + 60 \)
      This simplifies to:
    • \( 12x + 10y = 156 \)

  5. Solve for y.

    • From the original set of equations, you could isolate one variable after adding: Combine the similar terms: \( 10y = 156 - 12x \)

    Next, choose to isolate \( y \):

    • \( 10y = 156 - 12x \)
      To simplify, divide each term by 10:
    • \( y = \frac{156 - 12x}{10} \)
    • \( y = 15.6 - 1.2x \)

  6. Solve for x.

    • Use one of the original equations, substituting \( y \) back in: From the original equation \( 3x + 4y = 48 \), Substitute \( y \):
    • \( 3x + 4(15.6 - 1.2x) = 48 \)
    • \( 3x + 62.4 - 4.8x = 48 \) Combine like terms:
    • \( -1.8x + 62.4 = 48 \) Solve for \( x \):
    • \( -1.8x = 48 - 62.4 \)
    • \( -1.8x = -14.4 \)
    • \( x = 8 \)

Finally, using either original equation to solve for \( y \):

  • Substitute \( x = 8 \) back into \( 3x + 4y = 48 \):
  • \( 3(8) + 4y = 48 \)
  • \( 24 + 4y = 48 \)
  • \( 4y = 48 - 24 \)
  • \( 4y = 24 \)
  • \( y = 6 \)

Thus, the solution to the system of equations is:

  • \( x = 8 \)
  • \( y = 6 \)