Systems of Equations Word Problems on Graphs

A large pizza at Pizzi Inn costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza 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

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

• S + A = 530
  3S + 4A = 1740

• S + A = 530
  4S + 3A = 1740

• S + A = 1740
  3S + 4A = 530

• S + A = 1740
  4S + 3A = 530

Your family goes to The Stanford restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14.80, and some order steak for $17. If the total bill was $91, which system best represents the situation? 

• x + y = 6
  14.80x + 17y = 91

• x + y = 91
  14.80x + 17y = 6

• x + y = 6
  14.80y + 17x = 91

• x + y = 91
  14.80x+ 17y = 6

The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. Write a system of equations.

• 5q + 2z = 1.32
  1z = 0.75

• 5q + 2z = 1.32
  3q + 1z = 0.75

• q + z = 1.32
  q + z = 0.75

• 5q + 2z = 0.75
  3q + 1z = 1.32

What is the solution to the system of equations graphed below?

• No Solution

• Infinite Solutions

• One Solution: (0, 4)

• One Solution: (0, 6)

How many solutions will this system have?

• One

• Two

• No Solution

• Infinitely Many Solutions

•  a. y = ½ x + 2

  y = –x – 3  

• b. y = ½ x + 2

  y = x – 3

• c. y = –½ x – 3

      y = –x + 2   

• d. y = –½ x + 3

  y = x + 2

•    a. y = 2x + 4

  y = 3x + 1

• b. y = 2x + 4

  y = –3x + 1

     

• c. y = –2x + 1    

   y = –3x + 4 

• d. y = 2x + 1

  y = –3x + 4

Decide if the following statements are true or false about the graph.

Groups:

(a) True

,

(b) False

• The lines will eventually touch, so the system has one solution

• The slope(m) of the lines are equal

• The lines will not intersect, so the system has no solution

• The line are parallel, so the system has no solution

• The slopes are equal, so the system has infinitely many solutions

• The lines are perpendicular which means they will not ever cross.

How many solutions will this system have?

• One

• Two

• No Solution

• Infinitely Many Solutions