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Worksheet by Kuta Software LLC

Systems of Linear Inequalities Name___________________________________

Date________________ Period____©A [2d0j1d7` OKzuUtZaI jSdozfMtNwmanrXe] zLLLpCn.H a zAQlSls erQixg^hwtSsF irOedsmeErLvHeMdg.

-1-

Definition of a System of Linear Inequalities - A system of linear inequalities in two variablesconsists of at least two linear inequalities in the same variables.

1)

x

y

Graph the linear inequality yx. Where on the graph are the solutions tothe inequality?

2)

x

y

Graph the linear inequality yx. Where on the graph are the solutions tothe inequality?

3)

x

y

Graph both linear inequalities on the samegraph. yx yx Where on the graph are the solutions tothe system of inequalities?

4) The solutions of a system of linearinequalities are the __________________that are solutions to ________ inequalitiesin the system. On a graph the solutions to a system ofinequalities is the____________________of the half-planes or where the shadedregions ______________. WORD BANK- overlap - intersection - all- ordered pairs

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Worksheet by Kuta Software LLC-2-

Sketch the solution to each system of inequalities.

5) yx

x

x

y

6) yyx

x

y

7) yx

yx

x

y

8) yx

x

x

y

9) yx

yx

x

y

10) yyx

x

y

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Worksheet by Kuta Software LLC-3-

11) xyxy

x

y

12) xyxy

x

y

13) xyxy

x

y

14) xyxy

x

y

15) xyxy

x

y

16) xxy

x

y

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Worksheet by Kuta Software LLC-4-

17)

x

y

Which x-values make the ordered pair (x, ) a solution of the system ofinequalities represented by the graphbelow?

A) x B) xC) x D) x

18)

x

y

Which x-values make the ordered pair (x, ) a solution of the system ofinequalities represented by the graphbelow?

A) x B) xC) x D) x

19) In a community service program, students earn points for two tasks: painting over graffiti andpicking 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.

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Worksheet by Kuta Software LLC

Systems of Linear Inequalities Name___________________________________

Date________________ Period____©v x2x0_1M7c JKHuTtbao GSToGfJtAwjawrBeZ ELVLiCM.] O qAulVlY HrkiWgVh]tVsg Pr`e\sKe\rQvFefdk.

-1-

Definition of a System of Linear Inequalities - A system of linear inequalities in two variablesconsists of at least two linear inequalities in the same variables.

1)

x

y

Graph the linear inequality yx. Where on the graph are the solutions tothe inequality?

2)

x

y

Graph the linear inequality yx. Where on the graph are the solutions tothe inequality?

3)

x

y

Graph both linear inequalities on the samegraph. yx yx Where on the graph are the solutions tothe system of inequalities?

4) The solutions of a system of linearinequalities are the __________________that are solutions to ________ inequalitiesin the system. On a graph the solutions to a system ofinequalities is the____________________of the half-planes or where the shadedregions ______________. WORD BANK- overlap - intersection - all- ordered pairs

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Worksheet by Kuta Software LLC-2-

Sketch the solution to each system of inequalities.

5) yx

x

x

y

6) yyx

x

y

7) yx

yx

x

y

8) yx

x

x

y

9) yx

yx

x

y

10) yyx

x

y

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Worksheet by Kuta Software LLC-3-

11) xyxy

y

12) xyxy

x

y

13)

x

15)

x

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Worksheet by Kuta Software LLC-4-

17)

x

y

Which x-values make the ordered pair (x, ) a solution of the system ofinequalities represented by the graphbelow?

A) x B) xC) x D) x*

18)

x

y

Which x-values make the ordered pair (x, ) a solution of the system ofinequalities represented by the graphbelow?

A) x* B) xC) x D) x

19) In a community service program, students earn points for two tasks: painting over graffiti andpicking 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.