Download 9x + 2y = -9 18x – 5y = -18

SolvingSimultaneousLinearEquationsUsingtheSubstitutionMethod–MorePractice
Step1:Solve
9x+2y=-9
18x–5y=-18
x=(-9–2y)/9
x=-1–2/9y
Step2:Substitute
-1–2/9yforx,into18x–5y=-18
18(-1–2/9y)–5y=-18
-18–36/9y–5y=-18
-18–4y–5y=-18
-4y–5y=-18+18
-9y=0
y=0
Step3:SubstituteAgain
y=0into9x+2y=-9
9x+2(0)=-9
9x=-9
x=-1
Step4:Check
x=-1,y=0
9(-1)+2(0) 18(-1)–5(0)
=-9+2
=-18
=0
∴x=-1,y=0
Lesson12
Step1:Solve
[Fromhomeworkyesterday,question6]
5x–3y=3
3x–2y=0
5x=3+3y
x=3/5+3/5y
Step2:Substitute
3/5+3/5yforx,into3x–2y=0
3(3/5+3/5y)–2y=0
9/5+9/5y–2y=0
àMultiplyeverythingby5 or
9+9y–10y=0
9–y=0
y=9 Step3:SubstituteAgain
y=9into5x–3y=3
5x–3(9)=3
5x–27=3
5x=30
x=6
Step4:Check
x=6,y=9
5x–3y=3 3x–2y=0
5(6)–3(9) 3(6)–2(9)
=30–27
=18-18
=3 =0 ∴x=6,y=9
Homework:Ex1.Handout
àSolveusingfractions
9/5y–2y=-9/5
9/5y–10/5y=-9/5
-1/5y=-9/5
-5y=-45
y=9
Lesson13
SolvingSimultaneousLinearEquationsUsingtheSubstitutionMethod–EvenMorePractice
Step1:Solve
5x–4y=7
7x–2y=17
5x=7+4y
x=7/5+4/5y
Step2:Substitute
7/5+4/5yforx,into7x–2y=17
7(7/5+4/5y)–2y=17
49/5+28/5y–2y=17
àMultiplyeverythingby5*
or
àSolveusingfractions
49+28y–10y=85 28/5y–2y=17–49/5
18y=36
28/5y–10/5y=85/5–49/5
y=2 18/5y=36/5
90y=180
y=2
*Ifyoumultiply3/7by7,youcansimplifyitto3,sincethe7scancel;likewise,10/3×3=10
Step3:SubstituteAgain
y=2into5x–4y=7
5x–4(2)=7
5x–8=7
5x=15
x=3
Step4:Check
x=3,y=2
5x–4y=7 7x–2y=17
5(3)–4(2) 7(3)–2(2)
=15–8
=21–4
=7 =17 ∴x=3,y=2 Homework:Ex2.Handout
Lesson14
QuizMarkingScheme
Forallquestions:[7]
• Step1–Solveforonevariable[1]
• Step2–Substitution[1],distributiveproperty[1],processwork[1],solutionforone
variable[1]
• Step3–Substitutionforsolutiontoothervariable[1]
• Step4–Substitutionofbothvariablesintobothequationstocheckwork[1]
Forquestionswhereyouhavetodopre-worktogettoStep1[+2]
Forwordproblems:definitionofvariables[+0.5],statementthatanswersthequestion[+0.5]
QuizFormat
1. Doesnotrequireuseoffractions[7]
2. Requiresuseoffractions[7]
3. Requirespre-work[9]
4. Wordproblem[8]
Total:/31
ReviewandPreview–AQuestionfromToday’sHomework
4–(y–3)=x+3
(10+x)/3=2+(y–12)
Step1:Solve
4–y+3=x+3
7–y=x+3 4–y=x
Step2:Substitute
4–y=xintox=3y–40
4–y=3y–40
4+40=4y
44=4y
11=y
Step3:SubstituteAgain
y=11into4–y=x
3[(10+x)/3]=3[2+(y–12)]
10+x=6+3y-36
x=3y–40
4–11=x
-7=x
Step4:Check
x=-7,y=11
…
∴x=-7,y=11
SolvingSimultaneousLinearEquationsUsingtheSubstitutionMethod–WordProblems
Example1
Youandyourfriendpurchasechickenfingersandfriesforlunch.Youpay$11.20for3ordersof
chickenfingersand2ordersoffries.Yourfriendpays$10.40for1orderofchickenfingersand4
ordersoffries.Howmuchdoeseachitemcost?
Letcrepresentthecostofthechickenfingersandfrepresentthecostofthefries
3c+2f=11.20
1c+4f=10.40
…
∴Oneorderofchickenfingerscosts$2.40andoneorderoffriescosts$2.
Example2
Ifthelargerof2numbersissubtractedfrom6timesthesmallernumber,theresultis20.Iftwice
thelargernumberisaddedto4timesthesmallernumber,theresultis56.Findthenumbers.
Letxrepresentthelargernumberandyrepresentthesmallernumber
6y–x=20
2x+4y=56
…
∴Thelargernumberis16andthesmallernumberis6
Hints:
Q9
Admissionpricestoaconcertwere$20and$50.Thetotalamountofmoneypaidinoneticket
boothwas$9,550.Ticketsweresoldto320people.Howmanyofeachkindofticketweresold?
Letxrepresentthenumberof$20ticketsandyrepresentthenumberof$50tickets
x+y=320
20x+50y=9550
Q10
In3years,Alexwillbe3timesasoldashissisterNatasha.Ayearago,Alexwas7timesasoldas
Natasha.Howoldaretheynow?
LetarepresentAlex’spresentageandnrepresentNatasha’scurrentage
a+3=3(n+3)àa=3n+6
a–1=7(n–1)àa=7n–6
Homework:Handout(ExtraWordProblemsandMixedExercise)
àEx.3optional:forextrapractice
Quiz#2!
Lesson15
MoreWordProblems
Whilesomewordproblemsrequiretheuseofsimultaneouslinearequations,othersdonot.
Nevertheless,inbothcases,thevariablesmustbedefinedandthequestionmustbetranslated
intoequations.Ifthequestiondoesnotrequiretheuseofsimultaneouslinearequation,onlyone
variableshouldbedefined;allotherunknownquantitiesshouldbeexpressedbasedontheone
variablethathasbeendefined.
Example1
Thesumof4consecutivenumbersis50.Whatisthe3rdnumber?
Letxbethesmallestnumber
(x)+(x+1)+(x+2)+(x+3)=50
4x+6=50
4x=44
x=11
3rdnumber =x+2
=11+2
=13
rd
∴The3 numberis13
Example2
Thesumof3consecutiveevennumbersis72.Whatarethenumbers?
Letxbethesmallestnumber
(x)+(x+2)+(x+4)=72
3x+6=72
3x=66
x=22
∴The3numbersare22,24,and26
Example3
Hueyis11yearsolderthanDewey.Louieis3timestheageofDewey.Hueyis16yearsold.How
oldareDeweyandLouie?
LetdbeDewey’sage,andlbeLouie’sage
[Ask:Whoisolder?]
l=3d
h=d+11
l=3(5)
l=3d
l=15
h=16
∴Deweyis5andLouieis15
16=d+11
d=5
Example4
John’spresentageis3/4ofSherman’spresentage.In5years,John’sagewillbe4/5ofSherman’s
ageatthattime.WhatarethepresentagesofJohnandSherman?
LetjbeJohn’spresentageandsbeSherman’spresentage
Step1
j=3/4s
j+5=4/5(s+5)
Step2
3/4sforj,inj+5=4/5(s+5)
3/4s+5=4/5(s+5)
3/4s+5=4/5s+4 4(3/4s+5)=4(4/5s+4)
3s+20=16/5s+16
5(3s+20)=5(16/5s+16)
15s+100=16s+80
100–80=16s–15s
20=s
Step3
j=3/4s
=3/4(20)
=15
Step4
15=3/4(20)
=60/4
=20
15+5=4/5(20+5)
20=4/5(25)
=100/5
=20
∴Johnis15andShermanis20
Homework:Handout
Test!