01-10 Intro to Systems of Inequalities - Rancho High …

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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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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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___________________________________

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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

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