7-6:SYSTEMSOFLINEARINEQUALITIES

LessonObjectives:• Solvesystemsoflinearinequalitiesbygraphing• Modelreal-worldsituationsusingsystemsoflinearinequalities

EXAMPLE1:GRAPHINGANINEQUALITY

1. Solvebygraphing. ! > 2! − 5

3! + 4! < 12

i

Solvebygraphing.2.! < 2! − 3 3.6! + 8! < 32−2! + ! > 5 −4! + 6! < 24

EXAMPLE2:WRITINGASYSTEMOFINEQUALITIESFROMAGRAPH

i

i

4.Writeasystemofinequalitiesforeachofthefollowinggraphs.

Youcanmodelsomereal-worldsituationsbygraphinglinearinequalities.Whenyougraphreal-worldsituations,youoftenneedtoplanhowyouwillscaleeachaxis.Usethevaluesforthex-andy-interceptstodetermineyourscale.

EXAMPLE3:REAL-WORLDPROBLEMSOLVING

5.Azookeeperwantstofencearectangularhabitatforgoats.Thelengthofthehabitatshouldbeatleast80feet,andthedistancearounditshouldbenomorethan310feet.Whatarethepossibledimensionsofthehabitat?

ya2

III so

12 M

yeah ye Ex

Y

w GOATHABITAT

amis

21 2WE310go Go go bro180210 A

S length ft

6.Supposeyouwanttofencearectangularplot.Youwantthelengthofthegardentobeatleast50feetandtheperimetertobenomorethan140feet.Showallofthepossibledimensionsofthegarden. 7.Supposeyouneed$2.40inpostagetomailapackagetoafriend.Youhave9stamps,some20centsandsome34cents.Howmanyofeachdoyouneedtomailthepackage? 8.Supposeyouintendtospendnomorethan$60buyingbooks.Hardbackbookscost$12andpaperbackscost$5.Howmanybooksofeachtypecanyoubuy?

W GARDEN

Let b length

070 o so so so 4N So 60 To l

lengthCfa

POSTAGE

Let 2o stamps

y 34stamps 344 s

Xty E9

stamps

20 134y 2404

a

90 os o 2 4 6 8010 is 14204stamps

9.Inbasketballyouscore2pointsforafieldgoaland1pointforafreethrow.Supposethatyouhavescoredatleast6pointsineverygamethisseason,andhaveaseasonhighscoreof15pointsinonegame.Howmanyfieldgoalsandfreethrowscouldhavemadeinanyonegame?10.Supposeyouneedtouseatleast$1.00worthofstampstomailapackage.Youhaveasmany3centstampsasyouneed,butonlyfour32centstamps.Howmanyofeachstampcanyouuse?Writetwopossiblecombinationsthatyoucoulduse. 11.Agrandmotherwantstospendatleast$40butnomorethan$60onschoolclothesforhergrandson.T-shirtssellfor$10andpantssellfor$20.HowmanyT-shirtsandpantscouldshebuy?WritetwopossiblecombinationsofT-shirtsandpants.

BBALL POINTS14

utxg.fi InO Eire2xty26 4

2xty 152

µ 2 4 6 8 to 12 14

7 S FieldGoals

POSTAGE4236

Let X 3 stampsso

g 324stamps

24

332,8

stamps

713 6

o 2 4 6 8 w 12 143.12534stamps

coxes SHOPPING

Let x T shirts s

gpants Pants10 1 2 240 so

10 20560 I iIy2t

o a 3 I s 6 7

T shirts