SECONDARY MATH I // MODULE 5
SYSTEMS OF EQUATIONS AND INEQUALITIES – 5.10
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
5.10 Taken Out of Context
A Practice Understanding Task
Writeashoppingscenariosimilartothosein“ShoppingforCatsandDogs”tofiteachofthefollowingsystemsofequations.Thenusetheeliminationofvariablesmethodyouinventedin“CanYouGettothePoint,Too”tosolvethesystem.Someofthesystemsmayhaveinterestingorunusualsolutions.Seeifyoucanexplainthemintermsoftheshoppingscenariosyouwrote.
1.
3x + 4y = 235x + 3y = 31⎧ ⎨ ⎩
2.
2x + 3y =144x + 6y = 28
⎧ ⎨ ⎩
3.
3x + 2y = 209x + 6y = 35⎧ ⎨ ⎩
4.
4x + 2y = 85x + 3y = 9⎧ ⎨ ⎩
5. ThreeofCarlosandClarita’sfriendsarepurchasingschoolsuppliesatthebookstore.
Stanbuysanotebook,threepackagesofpencilsandtwomarkersfor$7.50.Janbuystwonotebooks,sixpackagesofpencilsandfivemarkersfor$15.50.Franbuysanotebook,twopackagesofpencilsandtwomarkersfor$6.25.Howmuchdoeachofthesethreeitemscost?
Explaininwordsorwithsymbolshowyoucanuseyourintuitivereasoningaboutthesepurchasestofindthepriceofeachitem.
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SECONDARY MATH I // MODULE 5
SYSTEMS – 5.10
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
5.10
READY Topic:SystemofinequalitiesForeachofthesystemsofinequalities,determineifthegivencoordinatesaresolutionstothesystem.(Showyourwork.)
1. ! ≤ 3! − 5! ≥ ! + 2
2.! > −2! + 9! ≥ 5! − 6 3. ! < − !
! ! + 9! > 6! − 10
a. 6, 10 b. 1, 4 c. 8, 15
a. −2,−5 b. −1, 12 c. 5, 0
a. −2,−5 b. 7, 3 c. −8, 10
SET Topic:DeterminingthenumberofsolutionsinasystemofequationsWriteeachequationinslope-interceptform.Basedonslope-interceptformoftheequationsdeterminewhetherthesystemofequationshaszero,one,orinfinitelymanysolutions.Howdoyouknow?4.3! − 4! = 13 ! = −3! − 7Howmanysolutions?Howdoyouknow?
5.3! − 3! = 3 ! − ! = 1Howmanysolutions?Howdoyouknow?
6.0.5! − ! = 30 0.5! − ! = −30Howmanysolutions?Howdoyouknow?
7.4! − 2! = −2 3! + 2! = −12Howmanysolutions?Howdoyouknow?
Solveeachsystem.Writeyoursolutionasanorderedpairorindicateifithasnosolutionsorinfinitelymanysolutions.
8.!+ !" = !!+ ! = !
9.!"+ ! = !! = !− ! 10.
! = !"+ !!"− !+ ! = !
READY, SET, GO! Name PeriodDate
38
SECONDARY MATH I // MODULE 5
SYSTEMS – 5.10
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
5.10
11.!"− !! = !!− !" = !!
12.! = !− !−!+ ! = ! 13.
−!"+ !" = −!!"+ !" = !!
14. −!"+ !" = !"!"+ ! = −! 15.
!"− !" = !!"+ !" = −!" 16.
−!"+ ! = −!!"− !− ! = !
17.!" = !+ !− !!!+ ! = ! 18.
!" = !"− !− !!!+
!!! = !
19.−!" = !"+ !!"− !" = −!
20.!+ ! = !"+ !!+ ! = !"− ! 21.
!" = −!!"+ !" = !" 22.
!"+ !" = !"− !!"− !" = !
39
SECONDARY MATH I // MODULE 5
SYSTEMS – 5.10
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
5.10
GO Topic:graphingtwovariableinequalities Graphthefollowinginequalities.Justifytheregionyoushadebyshowingatleastonepointintheregionasbeingasolutiontoeachinequality.
23.3! − 4! ≥ 12
24.! + 6! < 6
25.6! + 5! > 1
26.! − !! ! ≥ 3
27.Onthesamesetofaxesgraph ! < ! + 2and! > ! + 5.Dothesolutionsetsofthesetwoinequalitiesshareanypoints?Explain.
28.Onthesamesetofaxesgraph! < ! + 2and! < ! + 5.Dothesolutionsetsofthesetwo
inequalitiesshareanypoints?Explain.
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