Linear Systems Graphing and Applications

what can you say about these lines

• Consistent and Dependent

• Consistent and Independent

• Inconsistent and Dependent

• Inconsistent and Independent

WITHOUT GRAPHING
what can you say about these lines

• Consistent and Dependent

• Consistent and Independent

• Neither

• Inconsistent

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

Enterprise charges to rent compact cars for a fixed amount per day plus a fixed amount for each mile driven. Batman rented a car for 6 days, drove it 550 miles and spent $337. Superman rented the same car for 3 days, drove for 350 miles and spent $185. Set up the system. Let "d" represent the fixed charge per day and "m" represent the cost per mile.

• 6d + 550m = 337
  3d + 350m = 185

• 6d + 550m = 185
  3d + 350m = 337

• 6m + 550d = 337
  3m + 350d = 185

• 6m + 550d = 185
  3m + 350d = 337

Peyton Manning is comparing two weekend resort specials to relax at now that he has retired. Package A offers a 2-night stay and 3 meals that costs $195. Package B offers a 3-night stay and 5 meals that costs $300. Let "x" represent the cost per night and "y" represent the cost per meal.

• 2x + 3y = 195
  3x + 5y = 300

• 2x + 3y = 300
  3x + 5y = 195

• 2y + 3x = 195
  3y + 5x = 300

• 2y + 3x = 300
  3y + 5x = 195

You and a friend went to Los Tios for lunch. You order 2 tacos and 2 enchiladas. Your friend ordered 3 tacos and 1 enchilada. Your friend's bill was $4.00. You paid $4.80. Let "t" represent the price per taco and "e" represent the price per enchilada.

• 2t + 2e = 4.80
  3t + e = 4.00

• 2t + 2e = 4.00
  3t + e = 4.80

• 2e + 2t = 4.80
  3e + t = 4.00

• 2e + 2t = 4.00
  3e + t = 4.80

• No Solution

• (2, 2)

• (-1, 2)

• (-1, -2)

If a system of equations has infinitely many solutions, what does the graph look like? 

• intersecting lines

• parallel lines

• skew lines

• the same line (coinciding lines)

Lisa and Tammy are selling items at the craft show.  Which might be a reasonable solution from the graph showing the number of items sold when they both have earned the same amount?

• (1, 12)

• (3, 19)

• (5, 25)

• (0, 10)

Last season two running backs on the Steelers football team rushed a combined total of 1550 yards.  One rushed 4 times as many yards as the other.  Let x and y represent the number of yards each individual player rushed. Which system of equations could be used? 

• x + y = 1550
  y  = 4x

• x + y = 1550
  y = x + 4

• y - x = 1550
  y = 4x

• y = 1550 + x
  y = x + 4