NAME:___________________________
Math________,Period____________
Mr.Rogove
Date:__________
Learning Objective:Wewillsolvesystemsofequationsbysubstitution
(G8M4L24)
Concept Development:
SubstitutionMethodofSolvingSystemsofLinearEquations
Iftwoexpressionsareequaltothesamevalue,thentheycanbewrittenasequalto
eachother.
Examples:
3! = 4! + 2
! = 5! − 8
! = 6! + 3
! =!+5
STRATEGY:WhentouseSubstitutionMethod
1.WhenbothequationsareALREADYinslopeinterceptform.(i.e.yvariablehasbeenisolated)
2.Whenoneequationisinslope-interceptform.(y-variablehasbeen
isolated)
3.Whenx-variablehasbeenisolatedinoneequation.
4.Whenittakesonesteptoisolateavariableinoneoftheequations.
1
G8M4L24:SolvingSystemsofEquationsbySubstitution
NAME:___________________________
Math________,Period____________
Mr.Rogove
Date:__________
Guided Practice:
StepsforSolvingSystemsofEquationsbySubstitution
1.(Ifnecessary)Manipulateoneoftheequationstoisolateavariable(**ifyou’re
isolatingthey-variable,youwillbeconvertingyourequationtoslope-interceptform).
2.Rewritetheequationsubstitutingtheequivalentvalues,containingonlyone
variable.
3.Solvefortheoneremainingvariableinyourequation.
4.Solveforthesecondvariablebyreplacingyoursolutionfromstep3aboveinto
youroriginalequation.
5.Expressyouranswerintermsofanorderedpair.
2
! = 3! + 5
! = 8! + 3
! = 7! − 2
2! − 4! = 10
1
!
4 ! =!−7
!=
2! = −6! + 2
5
! = !+3
2
G8M4L24:SolvingSystemsofEquationsbySubstitution
NAME:___________________________
Math________,Period____________
Mr.Rogove
Date:__________
! = −2! + 11
4! = 5! − 1
3
2! = 3! + 9
! − 4! = 10
! = 3! + 4
3! − ! = 8
3! = 4! − 5
3! + ! = 4
G8M4L24:SolvingSystemsofEquationsbySubstitution
NAME:___________________________
Math________,Period____________
Mr.Rogove
Date:__________
Independent Practice:
Solveeachsystemofequationsusingsubstitution.
! = 3! − 5
! = 6! + 8
! = −3! + 1
−2! = 5! + 2
! = 4! + 9
3! = 2! − 17
! = −6! + 32
3! − 5! = 30
3
!−1
2
3! = ! + 2
7! − 8! = 112
! = −2! + 9
!=
4
G8M4L24:SolvingSystemsofEquationsbySubstitution
NAME:___________________________
Math________,Period____________
Mr.Rogove
Date:__________
Activating Prior Knowledge:
Wecantellhowmanysolutionsasystemhasbylookingattheslope:
! − ! = 12
3
!−5
4
3! − 4! = 20
! =!−7
!=
Closure:
Writeasystemofequationswith(4, −5)asitssolution.
Teacher Notes:
ThisisthesecondhalfofLesson27
HWisKhan:SystemsofEquationswithSubstitution
5
G8M4L24:SolvingSystemsofEquationsbySubstitution