Module4:LinearEqua5ons
TopicD:SystemsofLinearEqua5onsandTheirSolu5ons
Lesson4-29:WordProblems–
Wri5ngandSolvingSystemsof
LinearEqua5ons
Lesson4-29:WordProblems–Wri5ngandSolvingSystems
ofLinearEqua5ons
Purposefor •  Studentswritewordproblemsintosystemsof
Learning:
Essen5al
Ques5on(s):
Vocabulary:
linearequa5ons.
•  Studentssolvesystemsoflinearequa5ons
usingelimina5onandsubs5tu5onmethods.
•  Describehowwri5ngsystemsoflinear
equa5onshelpsustorepresentsitua5onsin
reallife.
•  Systemoflinearequa5ons
Discussion:Wri5ngandSolvingSystemsofLinearEqua5ons:
•  Inthislesson,youwillusemanyoftheskillslearnedinthismodule.
•  Youwill:
1.Definethevariablesasdescribedinawordproblem.
•  IfwedefineourvariableswecanbeCerrepresentthesitua5on
wehavebeengiven.
•  Let𝒙representonepartofthegivensitua1on
•  Let𝒚representtheotherpartofthegivensitua1on.
2.Writeasystemoflinearequa5onstorepresenttheinforma5onin
thewordproblem.(Hint:lookforkeywords.)
3.Solvethesystem.
•  decidewhichmethodforsolvingthesystemismostefficient.
•  ShouldIusesubs5tu5onorelimina5ontosolvethisproblem?
•  solvethesystem
4.Checksolu5oninbothequa5ons.
5.Writeaconcludingstatementthatanswerstheques5on.
Useasystemoflinearequa5onstosolvethisproblem.
Example1:(inyourstudentbooklet)
Thesumoftwonumbersis
361andthedifferencebetweenthetwo
173
1.Variables
numbersis
.Whatarethetwonumbers?
Ø  xrepresentsthefirstnumber {█𝑥+𝑦=361⁠𝑥
Ø  yrepresentsthesecond
−𝑦=173 number
2𝑥=534
2.Equa1on1:Sum(meansadd)
𝒙=𝟐𝟔𝟕
Ø 𝑥+𝑦=361
𝑥+𝑦=361
267+𝑦=361
𝒚=𝟗𝟒
Equa1on2:Difference(means
subtract)
Ø  𝑥−𝑦=173
{█𝑥+𝑦=361⁠𝑥−𝑦=173 3.Solvethesystem:
–  (useelimina5on)
SOLUTION:
(𝟐𝟔𝟕,𝟗𝟒)
Example1:(con5nued)
Thesumoftwonumbersis
361andthedifferencebetweenthetwo
173
numbersis
.Whatarethetwonumbers?
{█𝑥+𝑦=361⁠𝑥
4.Check:
−𝑦=173 Ø  InBOTHequa@ons
2𝑥=534
𝒙=𝟐𝟔𝟕
5.Writeaconcludingstatement
thatanswerstheques1on.
•  Thetwonumberswhose
sumis361anddifferenceis
173are(267and94).
𝑥+𝑦=361
267+𝑦=361
𝒚=𝟗𝟒
SOLUTION:
(𝟐𝟔𝟕,𝟗𝟒)
Check:
𝑥+𝑦=361
𝟐𝟔𝟕+𝟗𝟒=361
𝟑𝟔𝟏=361
True!ItChecks!
𝑥−𝑦=173
𝟐𝟔𝟕−𝟗𝟒=173
𝟏𝟕𝟑=173
True!ItChecks!
Example2:(inyourstudentbooklet)
356
Thereare
Grade8studentsatEuclid’sMiddleSchool.Thirty-fourmore
thanfour5mesthenumberofgirlsisequaltohalfthenumberofboys.How
manyboysareinGrade8atEuclid’sMiddleSchool?Howmanygirls?
Solu5on:(32,324)
5.)***Thereare32girls
and324boysingrade8at
Euclid’sMiddleSchool.
Example3:(inyourstudentbooklet)
Afamilymemberhassomefive-dollarbillsandone-dollarbillsintheirwallet.
18billsandatotalof$62.Howmanyofeachbilldoes
Altogethershehas
shehave?
Solu5on:(11,7)
5.)***Thefamilymemberhas11five
dollarbills,and7onedollarbillsfora
totalof$62.
Example4:(inyourstudentbooklet)
2boxesofpencilsand8 notebooksforschoolanditcosthim
Afriendbought
$11.Hewentbacktothestorethesamedaytobuyschoolsuppliesforhis
Solu5on:(2.50,0.75)
youngerbrother.Hespent$11.25on3boxesofpencilsand5
notebooks.Howmuchwould7notebookscost?
5.)Sevennotebookswillcost$5.25
(0.75*7)
Exercise1:(inyourstudentbooklet)
42animals.One
dayhecountsthelegsofallofhisanimalsandrealizeshehasatotalof114.
Afarmraisescowsandchickens.Thefarmerhasatotalof
Howmanycowsdoesthefarmerhave?Howmanychickens?
Solu5on:(15,27)
5.)Thefarmerhas15cowsand27
chickens.
Exercise2:(inyourstudentbooklet)
4 5mesthewidth.Theperimeteroftherectangleis
Thelengthofarectangleis
Solu5on:(18,4.5)
45 inches.Whatistheareaoftherectangle?
5.)Area=length*width
18*4.5
Theareaoftherectangleis81in.²
Exercise3:(inyourstudentbooklet)
𝑥and𝑦is127˚.Ifthemeasureof
∠𝑥is34˚morethanhalfthemeasureof∠
𝑦,whatisthemeasureofeach
Solu5on:(65,62)
Thesumofthemeasuresofangles
angle?
5.)Themeasureof∠𝒚is62°
andthemeasureof∠𝒙is
65°
LessonSummary:
•  Weknowhowtowriteinforma5onfromwordproblemsintoa
systemoflinearequa5ons.
•  Wecansolvesystemsoflinearequa5onsusingtheelimina5on
andsubs5tu5onmethods.
•  Whenwesolveasystemwemustclearlydefinethevariables
weintendtouse,considerwhichmethodforsolvingthe
systemwouldbemostefficient,checkouranswerandthink
aboutwhatitmeansincontext.Finally,weshouldcheckto
makesurewehaveansweredtheques5onposedinthe
problem.