Graphing Systems of Inequalities Study Notes

GRAPHING SYSTEMS OF INEQUALITIES

INDEPENDENT PRACTICE

  • Name: Brandon
  • Date: 1-9426
  • Pd:

Exercises: Graphing Systems of Inequalities and Solutions

Exercise 1

  1. Graph the system of inequalities:
    • y < 5
    • x + 3
    • 2x + 4y < 20
    • y > 2x - 4
    • 6x + 3y < 97
  2. Determine if each ordered pair represents a solution to the system:
    • a. (-3, 4) - Yes
    • b. (2, 5) - No
    • a. (2, 4) - Yes
    • b. (-3, 5) - No

Exercise 2

  • Use the graphed system of inequalities to answer a-c.
    • a. Write the system of inequalities represented on the graph:
    • y < 1x - 2
    • b. List three ordered pairs that are solutions to the system:
    • (2, 2)
    • (7, 2)
    • (5, 3)
    • c. List three ordered pairs that are not solutions to the system:
    • (-1, 7)
    • (-6, 4)
    • (6, 7)

Exercise 3

  • Statement: Jim has over 40 contacts saved in his phone.
    • The contacts consist of friends (y) and family (x).
    • Inequalities to represent the situation:
    • x + y > 40
    • y ext{ (friends) }
      eq 2x (number of friends is at least 2 times the number of family contacts)
    • Graph the inequalities to find the solution set.

Exercise 4

  1. Graph the system of inequalities:

    • y ext{ (unknown)}
      eq -6
    • x + 2y < 4
    • -x < 212 - x + 4
    • Determine if it's a valid inequality.

  2. Use the system of inequalities shown to answer a-c.

    • a. Write the system of inequalities represented:
    • Inequalities to deduce.
    • b. List three ordered pairs that are solutions to the system:
    • (-4, 12)
    • (-6, 9)
    • (-6, -6)
    • c. List three ordered pairs that are not solutions to the system:
    • (6, -4)
    • (8, 8)
    • (4, 10)

Exercise 5

  • Statement: Jessica bought hot dog buns and hamburger buns for a neighborhood cookout.
    • Total number of buns was less than 50.
    • Condition: More hot dog buns than hamburger buns.
  • System of inequalities to represent:
    • Let x = hamburger buns, y = hot dog buns.
    • Graph the solution set:
    • x + y < 50
    • y > x
    • b. Possible combination of buns:
    • 16 hamburger buns, 30 hot dog buns
    • c. Identify any nonsensical ordered pairs:
    • Any negative values or non-integer values.

Exercise 6

  • Aim: Model real-world situations using systems of inequalities.

  1. Scenario: A high school drama club is hosting a theater production.

    • Maximum of 800 tickets available for sale.
    • Ticket prices: $6 before the day of the show; $9 on the day of the show.
    • Expenses to cover: At least $5,000 to be made.
    • a. Write a system of inequalities to represent:
    • Total tickets inequality: x + y ext{ (where x = tickets sold, y = tickets on sale) } = 800
    • Revenue inequality: 6x + 9y ext{ (where x = $6 tickets, y = $9 tickets) } = 5000
    • b. Constraint: The club sells 440 tickets before the show.
    • Determine if enough tickets can still be sold that day:
    • 440 + x ext{ (additional tickets) } + 9 = 2640
    • Justification of expenses:
    • Remaining tickets: 360
    • 360 + x9 = 3240
    • Combined total: 5880 (meets expenses)

  2. Scenario: Edith babysits for x hours a week at $4/hour and works at the library for y hours at $8/hour.

    • She works no more than 15 hours a week.
    • Wants to earn at least $80 weekly.
    • System of inequalities to represent:
      • Babysitting hours: x + y ≤ 15
      • Earnings: 4x + 8y ≥ 80
    • Determine one combination of hours that allows Edith to meet requirements:
      • Ex: 2 hours babysitting, 10 hours library work.
      • Verification:
      • 2 + 10 = 12 ≤ 15
      • Earnings: (4/2) + (8/10) ≥ 80

Summary of Today's Lesson:

  • Focus: Understanding how inequalities represent real-world situations and how to graph them effectively to find solutions.
  • Emphasis on careful formulation of inequalities and accurate graphing techniques for visual representation of data constraints.

Sources: Maneuvering the Middle LLC, 2020