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.

CC

BY

Sty

liano

s M

ysta

kidi

s

http

s://f

lic.k

r/p/

75zt

WE

37

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.

-5

-5

5

5

-5

-5

5

5

-5

-5

5

5

-5

-5

5

5

-5

-5

5

5

-5

-5

5

5

40