
A.5 Systems of Inequalities
Presentation
•
Mathematics
•
8th Grade
•
Easy
Standards-aligned
Rabah Issa
Used 6+ times
FREE Resource
14 Slides • 29 Questions
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Systems of Inequalities

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Solutions
A solution is in the area where the shadings overlap
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Graphing Systems of Linear Inequalities
Learning Outcomes:
1. Be able to graph a system of linear inequalities
2. Identify solutions to systems of linear inequalities by graphing
4
Multiple Choice
Systems of Equations:
What is the solution to this system?
(1, -1)
(-1, 1)
(0, -2)
(2, 0)
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Multiple Choice
Graphing Linear Inequalities:
Consider the function y < 2x+3. Which is true?
The line would be solid with shading above.
The line would be dashed with shading above.
The line would be solid with shading below.
The line would be dashed with shading below.
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What is a System of Linear Inequalities?
A set of at least two linear inequalities in the same variables
To solve a system, you need to find the variable values that will make each inequality true at the same time
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Let's think about systems of equations for a moment...
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Open Ended
Which area (white, red, purple, blue) do you think represents the solution to this system of inequalities? Explain your reasoning.
Remember that a solution makes BOTH inequalities true at the same time.
13
Multiple Choice
Which point is a solution?
(0, 6)
(-3, 5)
(1, 0)
(-4, 3)
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Multiple Choice
Solution
Not a solution
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Multiple Choice
(0,-1)
(0,3)
(4,0)
(6,-2)
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Multiple Choice
Solid
Dashed
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Multiple Choice
y ≥ -x - 1 y < x + 4
y < -x - 1 y ≥ x + 4
y > -x - 1 y ≥ x + 4
y > -x - 1 y ≥ x + 3
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Multiple Choice
Solid or dashed line? Y ≥
Solid
Dashed
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Multiple Choice
y > 2x - 4 y < 2
y < 2x - 4 y < 2
y > 2x - 4 y < 2
y < 2x - 4 y < -2
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Multiple Choice
Solve the system of inequalities by graphing.
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Multiple Choice
Solve the system of inequalities by graphing.
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Multiple Choice
y≤-2x+5
y>2x+7
Which of the following is NOT a solution?
(-4, 2)
(-10, 7)
(-3, 0)
(-2, 6)
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Multiple Choice
Solve the system of inequalities by graphing. 8x +4y≥10 and 3x−6y>12
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Multiple Choice
Identify the graph represented by the following system of inequalities.
2x - y > 4
4x + 2y < 6
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Multiple Choice
Is (-2, 0) a solution to the system?
Solution
Not a solution
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Multiple Choice
(0, 0)
(2, -1)
(-2, -2)
(-5, 1)
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Multiple Choice
No solution
Infinite solutions
(-5, 5)
(5, -5)
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Systems of Inequalities Word Problems
Example:
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When solving inequality word problems, remember the key words and phrases that go along with each inequality symbol:
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Multiple Choice
Bobbi can work at most 20 hours next week, but she needs to earn at least $150. Her dog-walking job pays $6 per hour and her job as a car wash attendant pays $10 per hour.
Let x = # of hours dog-walking
Let y = # of hours at car wash
Which system of inequalities represents the scenario?
6x+10y≥150 x+y≤20
6x+10y≤150 x+y≥20
x+y≤150 6x+10y≥20
x+y≥150 6x+10y≤20
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Multiple Choice
Bobbi can work at most 20 hours next week, but she needs to earn at least $150. Her dog-walking job pays $6 per hour and her job as a car wash attendant pays $10 per hour.
Let x = # of hours dog-walking
Let y = # of hours at car wash
Which graph represents the system of inequalities?
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Multiple Choice
Suppose you can spend no more than 15 hours a week at your two jobs. Mowing lawns pays $3 an hour and babysitting pays $5 an hour. You need to earn at least $60 a week.
Let x = # of hours mowing
Let y = # of hours babysitting
Which graph represents the system of inequalities?
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Multiple Choice
Kate is selling bracelets and earrings on Etsy to make money for summer vacation. The bracelets (x) cost $2 and earrings (y) cost $3. She needs to make at least $100, but can only make up to 40 pieces of jewelry. Which inequalities represent this situation?
2x + 3y > 100
x + y ≤ 40
100x + 2y > 3
x + y ≤ 40
100x + 40y > 100
3x + 2y ≤ 40
3x + 2y > 100
x + y ≤ 40
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Multiple Choice
Luka and Dana are making cookies for the Westland Pantry. They only have up to 6 hours to bake! They can bake 32 chocolate chip cookies in an hour (x), and 20 snickerdoodle cookies in an hour (y). They need to make at least 150 cookies. Which inequalities represent the situation?
x + y ≥ 6 32x + 20y ≤ 150
x + y ≥ 632 x + 20y ≥ 150
x + y ≤ 6 32x + 20y ≤ 150
x + y ≤ 6 32x + 20y ≥ 150
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Multiple Choice
Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing
x+y≤300 7.5x+5.5y≥2000
x+y<300 7.5x+5.5y≥2000
x+y≤300 7.5x+5.5y≤2000
x+y>2000 7.5x+5.5y≤300
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Multiple Choice
Luka and Dana are making cookies for the Westland Pantry. They only have up to 6 hours to bake! They can bake 32 chocolate chip cookies in an hour (x), and 20 snickerdoodle cookies in an hour (y). They need to make at least 150 cookies. Which inequalities represent the situation?
x + y ≥ 6 32x + 20y ≤ 150
x + y ≥ 632 x + 20y ≥ 150
x + y ≤ 6 32x + 20y ≤ 150
x + y ≤ 6 32x + 20y ≥ 150
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Multiple Choice
Kate is selling bracelets and earrings on Etsy to make money for summer vacation. The bracelets (x) cost $2 and earrings (y) cost $3. She needs to make at least $100, but can only make up to 40 pieces of jewelry. Which inequalities represent this situation?
2x + 3y > 100
x + y ≤ 40
100x + 2y > 3
x + y ≤ 40
100x + 40y > 100
3x + 2y ≤ 40
3x + 2y > 100
x + y ≤ 40
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Multiple Choice
Cole is doing a basketball challenge for charity. In order to win money for the charity, he needs to score at least 20 points in less than 10 shots. If x is the number of 2-point shots, and y is the number of three point shots, which inequalities below represent the situation?
x + y < 10
2x + 3y ≥ 20
x + y ≤ 10
2x + 3y ≥ 20
x + y ≤ 10
2x + 3y > 20
x + y < 10
2x + 3y > 20
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Fill in the Blanks
Type answer...
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Multiple Choice
b + t < 15 3b + 6t > 66
b + t > 15 3b + 6t < 66
3b + 6t > 15 b + t < 66
3b + 6t < 15 b + t < 66
Systems of Inequalities

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