Systems Word Problems Graphing

At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. If a system of equations is written, which would be the correct representation of the 2 variables?

• t: # of tacos
  m: # of glasses of milk

• t: Cost of each taco
  m: Cost of each glass of milk

• t: total cost
  m: # of food items

• t: Cost of each glass of milk
  m: Cost of each taco

At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, t, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?

• t + n = 54
  t = 3n + 8

• t + n = 54
  n = 3t + 8

• t + n = 54
  t = 3n - 8

• t + n = 8
  t = 3n + 54

What is the solution?
(Hint:  Both lines are graphed over each other)

• One Solution

• No solution

• Infinitely Many Solutions

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

• intersecting lines

• the same line

• skew lines

• parallel lines

A large pizza at Rocky Lake Pizza costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Rocky Lake is $7.30 plus $0.65 for each topping. Which system of equations could be used to find the number of toppings when both companies cost the same amount? 

• y = 6.80 + .65x y=7.30+.90x

• x + y = 6.80 x + y = 7.30

• y = 6.80+.90x y = 7.30 + .65x

• y + .90x = 6.80 y + .65x = 7.30

CPA is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used?

• 1s + 3c = 38 2s + 3c = 52

• 3s + 1c = 38 3s + 2c = 52

• s + c = 38 s + c = 52

• 3s + 3c = 38 1s + 2c = 52

Kaleb graphed two lines in order to find the solution to a given system of equations. What is the solution?

• (-3,-8)

• (-8,-3)

• (3,-8)

• (8,3)

How many solutions?

• One Solution

• No solution

• Infinitely Many Solutions

At a college bookstore, Kassie purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, t, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?

• t + n = 54 t = 3n + 8

• t + n = 54 n = 3t + 8

• t + n = 54 t = 3n - 8

• t + n = 8 t = 3n + 54

Mark graphed two lines in order to find the solution to a given system of equations. What is the solution?

• (-1, 4)

• (1, -4)

• (-4, 1)

• (4, -1)