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
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