01-10 Intro to Systems of Inequalities - Rancho High School
Systems of Linear Inequalities
Name___________________________________
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Date________________ Period____
Definition of a System of Linear Inequalities - A system of linear inequalities in two variables consists of at least two linear inequalities in the same variables.
1)
y
2)
y
x
Graph the linear inequality yx.
x
Graph the linear inequality yx.
Where on the graph are the solutions to the inequality?
Where on the graph are the solutions to the inequality?
3)
y
x
Graph both linear inequalities on the same graph.
yx yx
Where on the graph are the solutions to the system of inequalities?
4) The solutions of a system of linear inequalities are the __________________ that are solutions to ________ inequalities in the system. On a graph the solutions to a system of inequalities is the____________________ of the half-planes or where the shaded regions ______________.
WORD BANK - overlap - intersection - all - ordered pairs
-1-
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Worksheet by Kuta Software LLC
Sketch the solution to each system of inequalities.
5) y x
x
y
x
7) y x
y x
y
x
9) yx y x
y
x
6) y yx
y
x
8) y x
x
y
x
10) y yx
y
x
-2-
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Worksheet by Kuta Software LLC
11) xy x y
y
x
12) x y x y
y
x
13) xy x y
y
x
14) x y x y
y
x
15) xy x y
y
x
16) x x y
y
x
-3-
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Worksheet by Kuta Software LLC
17)
y
18)
y
x
Which x-values make the ordered pair
(x, ) a solution of the system of
inequalities represented by the graph
below?
A) x C) x
B) x D) x
x
Which x-values make the ordered pair
(x, ) a solution of the system of
inequalities represented by the graph
below?
A) x C) x
B) x D) x
19) In a community service program, students earn points for two tasks: painting over graffiti and picking up trash. The following constraints are imposed on the program.
1) A student may not serve more than 10 total hours per week. 2) A student must serve at least 1 hour per week at each task.
Let g = the number of hours a student spends in a week painting over graffiti. Let t = the number of hours a student spends in a week picking up trash.
Write a system that represents the imposed constraints.
-4-
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Worksheet by Kuta Software LLC
Systems of Linear Inequalities
Name___________________________________
?v x2x0_1M7c JKHuTtbao GSToGfJtAwjawrBeZ ELVLiCM.] O qAulVlY HrkiWgVh]tVsg Pr`e\sKe\rQvFefdk.
Date________________ Period____
Definition of a System of Linear Inequalities - A system of linear inequalities in two variables consists of at least two linear inequalities in the same variables.
1)
y
2)
y
x
Graph the linear inequality yx.
x
Graph the linear inequality yx.
Where on the graph are the solutions to the inequality?
Where on the graph are the solutions to the inequality?
3)
y
x
Graph both linear inequalities on the same graph.
yx yx
Where on the graph are the solutions to the system of inequalities?
4) The solutions of a system of linear inequalities are the __________________ that are solutions to ________ inequalities in the system. On a graph the solutions to a system of inequalities is the____________________ of the half-planes or where the shaded regions ______________.
WORD BANK - overlap - intersection - all - ordered pairs
-1-
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Worksheet by Kuta Software LLC
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