Algebra 1 6-6 Independent Practice: Systems of Linear Inequalities
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by Matthew Richardson
| 7 Questions
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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?

A
B
C
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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.
Not necessarily; Even though the boundary lines are parallel, the inequalities may result in overlapping shaded regions.
Yes; The parallel boundary lines indicate that the graphs will have no points in common.
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Reflection: Math Success