Lesson4-29:WordProblems–Wri5ngandSolvingSystemsof

LinearEqua5ons

Module4:LinearEqua5onsTopicD:SystemsofLinearEqua5onsandTheirSolu5ons

Lesson4-29:WordProblems–Wri5ngandSolvingSystemsofLinearEqua5ons

PurposeforLearning:

Essen5alQues5on(s):

Vocabulary:

•  Studentswritewordproblemsintosystemsoflinearequa5ons.

•  Studentssolvesystemsoflinearequa5onsusingelimina5onandsubs5tu5onmethods.

•  Describehowwri5ngsystemsoflinearequa5onshelpsustorepresentsitua5onsinreallife.

•  Systemoflinearequa5ons

Discussion:Wri5ngandSolvingSystemsofLinearEqua5ons:•  Inthislesson,youwillusemanyoftheskillslearnedinthismodule.•  Youwill:

1.Definethevariablesasdescribedinawordproblem.•  IfwedefineourvariableswecanbeCerrepresentthesitua5onwehavebeengiven.

•  Let𝒙representonepartofthegivensitua1onrepresentonepartofthegivensitua1on•  Let𝒚representtheotherpartofthegivensitua1on.representtheotherpartofthegivensitua1on.

2.Writeasystemoflinearequa5onstorepresenttheinforma5oninthewordproblem.(Hint:lookforkeywords.)

3.Solvethesystem.• decidewhichmethodforsolvingthesystemismostefficient.•  ShouldIusesubs5tu5onorelimina5ontosolvethisproblem?•  solvethesystem

4.Checksolu5oninbothequa5ons.

5.Writeaconcludingstatementthatanswerstheques5on.

Useasystemoflinearequa5onstosolvethisproblem.Example1:(inyourstudentbooklet)

Thesumoftwonumbersis361andthedifferencebetweenthetwo

numbersis173.Whatarethetwonumbers?

1.VariablesØ  xrepresentsthefirstnumberØ  yrepresentsthesecond

number

2.Equa1on1:Sum(meansadd)Ø 𝑥+𝑦=361

Equa1on2:Difference(meanssubtract)

Ø  𝑥−𝑦=173

{█𝑥+𝑦=361𝑥−𝑦=173  3.Solvethesystem:

–  (useelimina5on)

{█𝑥+𝑦=361𝑥−𝑦=173  2𝑥=534𝒙=𝟐𝟔𝟕

𝑥+𝑦=361 267+𝑦=361�𝒚=𝟗𝟒

SOLUTION:(𝟐𝟔𝟕,𝟗𝟒)

Example1:(con5nued)

Thesumoftwonumbersis361andthedifferencebetweenthetwo

numbersis173.Whatarethetwonumbers?4.Check:

Ø  InBOTHequa@ons

5.Writeaconcludingstatementthatanswerstheques1on.

•  Thetwonumberswhosesumis361anddifferenceis173are(267and94).

{█𝑥+𝑦=361𝑥−𝑦=173  2𝑥=534𝒙=𝟐𝟔𝟕

𝑥+𝑦=361 267+𝑦=361�𝒚=𝟗𝟒

SOLUTION:(𝟐𝟔𝟕,𝟗𝟒)

𝑥+𝑦=361 𝟐𝟔𝟕+𝟗𝟒=361 𝟑𝟔𝟏=361

True!ItChecks!

𝑥−𝑦=173 𝟐𝟔𝟕−𝟗𝟒=173 𝟏𝟕𝟑=173

True!ItChecks!

Check:

Example2:(inyourstudentbooklet)

Thereare356Grade8studentsatEuclid’sMiddleSchool.Thirty-fourmorethanfour5mesthenumberofgirlsisequaltohalfthenumberofboys.HowmanyboysareinGrade8atEuclid’sMiddleSchool?Howmanygirls?

5.)***Thereare32girlsand324boysingrade8atEuclid’sMiddleSchool.

Solu5on:(32,324)

Example3:(inyourstudentbooklet)Afamilymemberhassomefive-dollarbillsandone-dollarbillsintheirwallet.

Altogethershehas18billsandatotalof$62.Howmanyofeachbilldoesshehave?

5.)***Thefamilymemberhas11fivedollarbills,and7onedollarbillsforatotalof$62.

Solu5on:(11,7)

Example4:(inyourstudentbooklet)

Afriendbought2boxesofpencilsand8 notebooksforschoolanditcosthim

$11.Hewentbacktothestorethesamedaytobuyschoolsuppliesforhis

youngerbrother.Hespent$11.25on3boxesofpencilsand5

notebooks.Howmuchwould7notebookscost?

Solu5on:(2.50,0.75)

5.)Sevennotebookswillcost$5.25(0.75*7)

Exercise1:(inyourstudentbooklet)

Afarmraisescowsandchickens.Thefarmerhasatotalof42animals.One

dayhecountsthelegsofallofhisanimalsandrealizeshehasatotalof114.Howmanycowsdoesthefarmerhave?Howmanychickens?

Solu5on:(15,27)

5.)Thefarmerhas15cowsand27chickens.

Exercise2:(inyourstudentbooklet)

Thelengthofarectangleis4 5mesthewidth.Theperimeteroftherectangleis

45 inches.Whatistheareaoftherectangle?

Solu5on:(18,4.5)

5.)Area=length*width18*4.5

Theareaoftherectangleis81in.²

Exercise3:(inyourstudentbooklet)

Thesumofthemeasuresofangles𝑥and𝑦is127˚.Ifthemeasureof

∠𝑥is34˚morethanhalfthemeasureof∠𝑦,whatisthemeasureofeachangle?

Solu5on:(65,62)

5.)Themeasureof∠𝒚is62°is62°andthemeasureof∠𝒙isis65°

LessonSummary:

•  Weknowhowtowriteinforma5onfromwordproblemsintoasystemoflinearequa5ons.

•  Wecansolvesystemsoflinearequa5onsusingtheelimina5on

andsubs5tu5onmethods.•  Whenwesolveasystemwemustclearlydefinethevariables

weintendtouse,considerwhichmethodforsolvingthesystemwouldbemostefficient,checkouranswerandthinkaboutwhatitmeansincontext.Finally,weshouldchecktomakesurewehaveansweredtheques5onposedintheproblem.