systems of equations...
TRANSCRIPT
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SystemsofEquationsPREALGEBRA
1
SolvingSystemsofEquations(PreAlgebraVersion)
Matchtheoperationwiththecorrectinverse
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SystemsofEquationsPREALGEBRA
2
REVIEW:Steps to Solving an Equation
SolvingEquationsMixedPractice
"Ido"*Watchasyouseemesolvethisproblem.*Listentomythoughtprocess.
j+5=j7
ClicktheproblemtoviewthePencast.
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SystemsofEquationsPREALGEBRA
3
SolvingEquationsMixedPractice
"Ido"*Watchasyouseemesolvethisproblem.*Listentomythoughtprocess.
9(w+1)=3w15
ClicktheproblemtoviewthePencast.
SolvingEquationsMixedPractice
"Wedo"3.3g+12=6g3 4.45=9(e+8)
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SystemsofEquationsPREALGEBRA
4
SolvingEquationsMixedPractice
"Wedo"5.4(y8)=12 6.24=4(h7)
2
SolvingEquationsMixedPractice
"Youdo"Findthesolutiontothenextfollowingproblems.
9.35=7t 10.3h+5=2h9
11.6u=21u 12.12k+13=8k+33
5 414 31 53
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SystemsofEquationsPREALGEBRA
5
Nowanswertheremainingproblemsonyourworksheet
(allthequestionswedidnotdotogetherinclass)
SolvingEquationsMixedPractice
SolvingSystemsofEquationsPreRequisiteWork
SlopeInterceptForm
IdentifytheslopeIdentifytheyintercept
Writeanequationiny=mx+bform
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SystemsofEquationsPREALGEBRA
6
Findtheslopefortheseequations:
a.y=6x+5b. y=3x7c.y=14+9x
Findtheyinterceptfortheseequations:
a.y=6x+5b. y=3x7c.y=14+9x
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SystemsofEquationsPREALGEBRA
7
Canyouwritetheequations?
1.slope=4yintercept=3
Equation:y=4x3
2.slope=3yintercept=7
Equation:y=3x+7
3.slope=0yintercept=5
Equation:y=0x+5
y=5
Writeeachequationinslopeinterceptform
(y=mx+b)
A.x+y=4 B.3x6y=9
C.4x+y3=0 D.xy+4=6
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SystemsofEquationsPREALGEBRA
8
Writeeachequationinslopeinterceptform
(y=mx+b)
E.x+y=0 F.x+3y3=0
G.xy=0 H.2x+3y=6
Writeeachequationinslopeinterceptform
(y=mx+b)
I.5(x+3+y)=10x J.2x+3y4=x+5
K.y0.5=0 L.y=2
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SystemsofEquationsPREALGEBRA
9
Homeworkony=mx+b(studenthomework)
Homeworkony=mx+b(studenthomework)
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SystemsofEquationsPREALGEBRA
10
SolvingSystemsofEquationsPreRequisiteWork
GraphingLinearEquations
Createagraphusingslopeinterceptform
ClickonthegraphtoopenanotherNotebookLessonongraphingusingy=mx+b
HomeworkonGraphing
StudentPracticePage
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SystemsofEquationsPREALGEBRA
11
SystemsofEquations
SolvingGraphically
Whichtwoequations,whengraphed,willpassthroughthepoint(1,2)?
y=x+1
y=x+2
y=x+3
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SystemsofEquationsPREALGEBRA
12
2=1+1y=x+1
2=1+3y=x+3
Whereelsewillthelinescross?
y=x+1
y=x+3
Systemsofequations
pointofintersection
TheONLYsolutiontothesystemsofequations:x=1andy=2
(1,2)
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SystemsofEquationsPREALGEBRA
13
www.moviesulike
www.gr8movies
Systemsofequationsintherealworld
www.moviesulikecharges$3todownloadamovie.
Writeanequationforeachwebsite.
www.gr8movieschargesasignupfeeof$3and$2permovie.
Graphtheequationsandfindthepointofintersection
y=3x
y=2x+3
(__,__)
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SystemsofEquationsPREALGEBRA
14
x=3
y=9
y=3x
y=2x+3
(3,9)
Pointofintersection(3,9)
Whatdoesthistellyou?
?
?
Whichwebsitewouldyouchooseifyouwantedtobuy:
a)2movies
b)3movies
c)5movies
y=3x
y=2x+3
(3,9)
Whichwebsite?
www.moviesulike
www.gr8movies
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SystemsofEquationsPREALGEBRA
15
Nowyoutrypg.401#8
y=2x1y=x+1
y=2x+3y=x3
Nowyoutrypg.401#9
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SystemsofEquationsPREALGEBRA
16
y=x + 2y=x+5
Nowyoutrypg.401#10
Practice Problems for the Students
Click graph to activate worksheet
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Attachments
GraphingLinearEquationsusingSlopeIntercept.notebook
SolvingSystemsbyGraphingPreAlgebraKutaSotwareworksheet.pdf
GraphingLinesinSlopeInterceptFormKutaSoftwareworksheet.pdf
images/image1.jpeg
images/blank-graph[1].gif
settings.xml
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assessment.xml
page0.svg
Feb 2-10:08 PM Graphing Linear Equations For each question... 1. Solve the equation for y. If the variable y is missing, solve for x. 2. Calculate the slope. 3. Calculate the y-intercept. 4. Graph on a coordinate axis.
page10.svg
Feb 2-10:09 PM 1. 4x + 2y = 12 slope = y-intercept =
page8.svg
Feb 2-10:09 PM 2. 6x - y = 7 slope = y-intercept =
page9.svg
Feb 2-10:09 PM 3. 3x + 5y = 10 slope = y-intercept =
page7.svg
Feb 2-10:09 PM 4. -5x + 4y = -8 slope = y-intercept =
page6.svg
Feb 2-10:09 PM 5. y = 5 slope = y-intercept =
page5.svg
Feb 2-10:09 PM 6. -y = 1/3x - 2 slope = y-intercept =
page4.svg
Feb 2-10:09 PM 7. x + 4 = 0 slope = y-intercept =
page3.svg
Feb 2-10:09 PM 8. -3y = -4x slope = y-intercept =
page2.svg
Feb 2-10:09 PM 9. 9y = 10 slope = y-intercept =
page1.svg
Feb 2-10:09 PM 10. y + -7 = 13 slope = y-intercept =
SMART Notebook
-
Kuta Software - Infinite Pre-Algebra Name___________________________________
Period____Date________________Solving Systems of Equations by Graphing
Solve each system by graphing.
1)
y
=
5
x
2
y
=
x
+ 4
5 4 3 2 1 0 1 2 3 4 5
5
4
3
2
1
2
3
4
5
2)
y
=
x
+ 3
y
=
1
4
x
2
5 4 3 2 1 0 1 2 3 4 5
5
4
3
2
1
2
3
4
5
3)
y
=
4
x
+ 2
y
=
4
x
+ 4
5 4 3 2 1 0 1 2 3 4 5
5
4
3
2
1
2
3
4
5
4)
y
=
4
3
x
+ 3
y
=
x
4
5 4 3 2 1 0 1 2 3 4 5
5
4
3
2
1
2
3
4
5
-
5)
y
=
x
4
y
=
3
2
x
+ 1
5 4 3 2 1 0 1 2 3 4 5
5
4
3
2
1
2
3
4
5
6)
y
=
7
x
4
y
=
7
x
+ 2
5 4 3 2 1 0 1 2 3 4 5
5
4
3
2
1
2
3
4
5
7)
y
=
7
2
x
+ 4
y
=
7
2
x
+ 2
5 4 3 2 1 0 1 2 3 4 5
5
4
3
2
1
2
3
4
5
8)
y
=
1
2
x
+ 2
y
=
7
4
x
3
5 4 3 2 1 0 1 2 3 4 5
5
4
3
2
1
2
3
4
5
-
Kuta Software - Infinite Pre-Algebra Name___________________________________
Period____Date________________Solving Systems of Equations by Graphing
Solve each system by graphing.
1)
y
=
5
x
2
y
=
x
+ 4
5 4 3 2 1 0 1 2 3 4 5
5
4
3
2
1
2
3
4
5
(1
, 3
)
2)
y
=
x
+ 3
y
=
1
4
x
2
5 4 3 2 1 0 1 2 3 4 5
5
4
3
2
1
2
3
4
5
(4
, 1
)
3)
y
=
4
x
+ 2
y
=
4
x
+ 4
5 4 3 2 1 0 1 2 3 4 5
5
4
3
2
1
2
3
4
5
No solution
4)
y
=
4
3
x
+ 3
y
=
x
4
5 4 3 2 1 0 1 2 3 4 5
5
4
3
2
1
2
3
4
5
(3
, 1
)
-
5)
y
=
x
4
y
=
3
2
x
+ 1
5 4 3 2 1 0 1 2 3 4 5
5
4
3
2
1
2
3
4
5
(2
, 2
)
6)
y
=
7
x
4
y
=
7
x
+ 2
5 4 3 2 1 0 1 2 3 4 5
5
4
3
2
1
2
3
4
5
No solution
7)
y
=
7
2
x
+ 4
y
=
7
2
x
+ 2
5 4 3 2 1 0 1 2 3 4 5
5
4
3
2
1
2
3
4
5
No solution
8)
y
=
1
2
x
+ 2
y
=
7
4
x
3
5 4 3 2 1 0 1 2 3 4 5
5
4
3
2
1
2
3
4
5
(4
, 4
)
SMART Notebook
-
Kuta Software - Infinite Pre-Algebra Name___________________________________
Period____Date________________Graphing Lines in Slope-Intercept Form
Sketch the graph of each line.
1)
y
=
8
x
4
6 5 4 3 2 1 0 1 2 3 4 5 6
6
4
2
2
4
6
2)
y
=
x
+ 5
6 5 4 3 2 1 0 1 2 3 4 5 6
6
4
2
2
4
6
3)
y
=
2
x
6 5 4 3 2 1 0 1 2 3 4 5 6
6
4
2
2
4
6
4)
x
= 4
6 5 4 3 2 1 0 1 2 3 4 5 6
6
4
2
2
4
6
5)
y
=
3
2
x
+ 3
6 5 4 3 2 1 0 1 2 3 4 5 6
6
4
2
2
4
6
6)
y
=
1
5
x
4
6 5 4 3 2 1 0 1 2 3 4 5 6
6
4
2
2
4
6
-
7)
y
=
2
3
x
3
6 5 4 3 2 1 0 1 2 3 4 5 6
6
4
2
2
4
6
8)
y
=
3
2
x
+ 2
6 5 4 3 2 1 0 1 2 3 4 5 6
6
4
2
2
4
6
9)
y
=
x
6 5 4 3 2 1 0 1 2 3 4 5 6
6
4
2
2
4
6
10)
y
=
4
5
x
5
6 5 4 3 2 1 0 1 2 3 4 5 6
6
4
2
2
4
6
11)
y
=
2
5
x
+ 3
6 5 4 3 2 1 0 1 2 3 4 5 6
6
4
2
2
4
6
12)
y
=
9
4
x
+ 4
6 5 4 3 2 1 0 1 2 3 4 5 6
6
4
2
2
4
6
-
Kuta Software - Infinite Pre-Algebra Name___________________________________
Period____Date________________Graphing Lines in Slope-Intercept Form
Sketch the graph of each line.
1)
y
=
8
x
4
6 5 4 3 2 1 0 1 2 3 4 5 6
6
4
2
2
4
6
2)
y
=
x
+ 5
6 5 4 3 2 1 0 1 2 3 4 5 6
6
4
2
2
4
6
3)
y
=
2
x
6 5 4 3 2 1 0 1 2 3 4 5 6
6
4
2
2
4
6
4)
x
= 4
6 5 4 3 2 1 0 1 2 3 4 5 6
6
4
2
2
4
6
5)
y
=
3
2
x
+ 3
6 5 4 3 2 1 0 1 2 3 4 5 6
6
4
2
2
4
6
6)
y
=
1
5
x
4
6 5 4 3 2 1 0 1 2 3 4 5 6
6
4
2
2
4
6
-
7)
y
=
2
3
x
3
6 5 4 3 2 1 0 1 2 3 4 5 6
6
4
2
2
4
6
8)
y
=
3
2
x
+ 2
6 5 4 3 2 1 0 1 2 3 4 5 6
6
4
2
2
4
6
9)
y
=
x
6 5 4 3 2 1 0 1 2 3 4 5 6
6
4
2
2
4
6
10)
y
=
4
5
x
5
6 5 4 3 2 1 0 1 2 3 4 5 6
6
4
2
2
4
6
11)
y
=
2
5
x
+ 3
6 5 4 3 2 1 0 1 2 3 4 5 6
6
4
2
2
4
6
12)
y
=
9
4
x
+ 4
6 5 4 3 2 1 0 1 2 3 4 5 6
6
4
2
2
4
6
SMART Notebook
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