Solving Pairs of Linear Equations

Michelangelo decided to order Pizza Hut last night. He purchased 3 pizzas and 2 orders of breadsticks for a total of $29.50. Donatello ordered 2 pizzas and 3 orders of breadsticks last Sunday for a total of $23. Set up a system. Let "p" represent the price per pizza and "b" represent the price of an order of breaksticks.

• 3p + 2b = 29.50
  2p + 3b = 23

• 3p + 2b = 23
  2p + 3b = 29.50

• 3b + 2p = 29.50
  2b + 3p = 23

• 5bp = 29.50
  5bp = 23

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes.  How long does it take her to do a haircut?
3x + 2y = 315
2x + 4y = 450

• 45 minutes

• 90 minutes

• 60 minutes

• 30 minutes

John was 20 feet away and was running 5 feet per minute. Alex was 50 feet away and was 3 feet per minute. Write a system of two equations for this situation?

• y = 5x + 20

  y = 3x + 50

• y = 20x + 5

  y = 50x + 3

• y = 5x + 50

  y = 2x + 20

• y = 50x + 5

  y = 20x + 3

Four times a number minus three times another number is thirteen. The sum of the two numbers is twelve. What are the two numbers? Use a system of equations to solve the problem.

• 3 and 9

• -3 and 15

• 5 and 7

• -5 and 17

You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. At the end of the night you made a total of $78.50. You sold a total of 87 hot dogs and sodas combined. You must report the number of hot dogs sold and the number of sodas sold. How many hot dogs were sold and how many sodas were sold?

• x + y = 78.50

• 1.50x + 0.50y = 87

• 1.50x + 0.50y = 78.50

  x + y = 87

• x + 0.50y = 87

The zoo has 11 tigers and zebras on display. The number of tigers is one less than twice the number of zebras. Write a system of equations if t = number of tigers and z = number of zebras.

The difference of two numbers is 3. Their sum is 13. Find the numbers.

• Caroline can order 12 games from Plan A & 6 games from Plan B.

• If Caroline orders 12 games each month, both plans will cost $6.

• Caroline can order 6 games from Plan A & 12 games from Plan B.

• If Caroline orders 6 games each month, both plans will cost $12.

How many solutions will this system have?

• No solution

• One Solution

• Infinitely Many Solutions