Algebra 1 6-6 Complete Lesson: Systems of Linear Inequalities
By Matt Richardson
Last updated about 2 years ago
23 Questions
Note from the author:
A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.
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1.
Solve It! You want to buy at least 6 new ring tones from a website, but you cannot spend more than $15. How many premium ring tones and how many top-10 ring tones can you buy? Explain how you found your answer.
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Problem 1 Got It? What is the graph of the system?
Include all relevant graph detail.
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Problem 2 Got It? What system of inequalities is represented by the graph? Select 2 inequalities to build the system.
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Problem 2 Got It? Reasoning: In the previous item, is the point where the boundary lines intersect a solution of the system? Explain.
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Problem 3 Got It? You want to build a fence for a rectangular dog run. You want the run to be at least 10 ft wide. The run can be at most 50 ft long. You have 126 ft of fencing. What is a graph showing the possible dimensions of the dog run? Include all relevant graph detail.
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Graph the system on the canvas below by hand, without the aid of a graphing utility.
After that, graph the system on the embedded Desmos graphing calculator above and edit your graph, as necessary.
Graph precisely and include important graph detail: label axes and indicate their scale, include arrows at the ends of solid or dashed boundary lines, shade one side or the other of each boundary line in the system. Use a shading technique that makes it easy to determine which regions are shaded once, twice, and not at all. If you need assistance, please ask.
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What system of inequalities is represented by the graph?
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8.
Cherries cost $4/lb. Grapes cost $2.50/lb. You can spend no more than $15 on fruit, and you need at least 4 lb in all. What is a graph showing the amount of each fruit you can buy?
Graph precisely and include important graph detail: label axes and indicate their scale, include arrows at the ends of solid or dashed boundary lines, shade one side or the other of each boundary line in the system. Use a shading technique that makes it easy to determine which regions are shaded once, twice, and not at all. If you need assistance, please ask.
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Vocabulary: How can you determine whether an ordered pair is a solution of a system of linear inequalities?
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Reasoning: Suppose you are graphing a system of two linear inequalities, and the boundary lines for the inequalities are parallel. Does that mean that the system has no solution? Explain.
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12.
Review Lesson 6-5: Graph the linear inequality. Include all relevant graph detail.
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Review Lesson 6-5: Graph the linear inequality. Zoom and pan your graph to establish an appropriate viewing window.
info
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Review Lesson 1-2: Match the simplified expressions on the left with their equivalent expressions on the right. Not all simplified expressions will be used.
- 4
- 77
- 12
- 15
- 90
- 113
- (1 + 3)² - (1 + 3)
- 4³ + 5² + (4 - 3)¹
- 7² + 2(3³ + 5)
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Review Lesson 6-5: Graph the linear inequality. Include all relevant graph detail.
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Vocabulary Review: Identify the system of equations.
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18.
Use Your Vocabulary: Complete the sentence with bounds, boundary, or border. Type only the word in your response.
The landscaper planted a __?__ of flowers along the sidewalk.
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Use Your Vocabulary: Complete the sentence with bounds, boundary, or border. Type only the word in your response.
The __?__ line on the map between countries is shown.
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20.
Use Your Vocabulary: Complete the sentence with bounds, boundary, or border. Type only the word in your response.
The ball bounced out of __?__.
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Use Your Vocabulary: Which ordered pair is on the boundary of the inequality?
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Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.
For a refresher on the Cornell note-taking system, click here.
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Reflection: Math Success
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