Practice: Solving Systems of Equations (3 Different Methods)

Transcription

1 -1- h AKEuotma ds7oofttlwoasrsew klglvch. Q laylly nroirgxhjtpsk rmeisqevravie9d.i U JMzaGdVex gw5ictuh7 iintfsi7n7iltler 9A7lmgLevb1rIai o1c.l Worksheet by Kuta Software LLC Da Vinci Design / Math 9 Practice: Solving Systems of Equations (3 Different Methods) Solve each system by substitution. ID: 1 Name Date 1) x + 3y = x + y = 1 ) x y = y = 3) 1x y = 7x + y = 3 ) 5x + y = 3x + y = Solve each system by elimination. 5) x y = 5x + 3y = 9 ) 15x + 9y = 7 5x y = 17 7) 7x y = 3 x + y = 1 ) 3x y = x 5y = 1 Solve each system by graphing. 9) y = 5 7 x + ) x = 7 y = x + 9 y = 1 7 x 0 0

2 -- d eksuutrao LSoohfWtnwXagre olml5cb.m pailalp yr9iwgfhutasx qrtexs0elrwveuda.v J TMbaNdev MwTi7tHh5 uionfviznrivtaei XAnl1gTeYbarnal w1t.h Worksheet by Kuta Software LLC 11) The senior classes at High School A and High School B planned separate trips to the state fair. The senior class at High School A rented and filled vans and buses with 7 students. High School B rented and filled 5 vans and buses with 117 students. Every van had the same number of students in it as did the buses. How many students can a van carry? How many students can a bus carry? 1) New York City is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 1 van and buses with 3 students. High School B rented and filled 9 vans and 3 buses with students. Every van had the same number of students in it as did the buses. How many students can a van carry? How many students can a bus carry? 13) A boat traveled 0 miles downstream and back. The trip downstream took 7 hours. The trip back took 1 hours. Find the speed of the boat in still water and the speed of the current. 1) A boat traveled 5 miles downstream and back. The trip downstream took 1 hours. The trip back took hours. What is the speed of the boat in still water? What is the speed of the current?

3 HKeuhtmac uswoofdtowsafrkej RLQLPCC.3 z hahl5lw rziigrhct0s7 drueasqejryv3etda.k p qma0dted nweiktkh1 RICnDfbibnjietoeK JAClWgGefbarkaC n Worksheet by Kuta Software LLC Answers to Practice: Solving Systems of Equations (3 Different Methods) (ID: 1) 1) (1, ) ) (1, ) 3) Infinite number of solutions ) (, ) 5) (, 7) ) ( 3, ) 7) (1, ) ) (, ) 9) ( 7, 1) ) (7, ) 11) Van: 15, Bus: 1 1) Van: 1, Bus: 5 13) boat: 30 mph, current: mph 1) boat: 1 mph, current: 9 mph

4 -1- t skuultea 3SMoUftQwUaQrneD ilnlfcw.c y raglhlp orjiogehhtbsl krhecsbewrnvceldd.d I VMcaGdweE HwaiXtThn yiangfkinnriatveg cavlhgferb7rgad G1g. Worksheet by Kuta Software LLC Da Vinci Design / Math 9 Practice: Solving Systems of Equations (3 Different Methods) Solve each system by substitution. ID: Name Date 1) x + y = x y = 1 3) x + y = 17 7x y = ) x y = 7 3x + y = 1 ) x + 7y = 1 x + y = Solve each system by elimination. 5) x + y = 9x + y = 7) 5x y = x + 3y = 5 ) x y = 1x + 5y = ) x y = 1 5x + y = 11 Solve each system by graphing. 9) y = 9 x + 7 y = 9 x 5 ) y = 3 x 9 y = 3x + 0 0

5 -- O jkgudtmaf JSkoHfXtZwLarneB XLlLsC0.o j OAblgl5 UrlilgYhwths7 sregs1errpvgedh.q r 5MoadHew Hwi3tGhD HIdnOfzi7nqiztCeH 0AmlUgXelbxrsa0 f1z.x Worksheet by Kuta Software LLC 11) The school that Jaidee goes to is selling tickets to the annual talent show. On the first day of ticket sales the school sold senior citizen tickets and 11 student tickets for a total of $190. The school took in $ on the second day by selling 5 senior citizen tickets and 1 student tickets. Find the price of a senior citizen ticket and the price of a student ticket. 1) The senior classes at High School A and High School B planned separate trips to the indoor climbing gym. The senior class at High School A rented and filled 1 vans and 9 buses with 35 students. High School B rented and filled 5 vans and 3 buses with 155 students. Every van had the same number of students in it as did the buses. How many students can a van carry? How many students can a bus carry? 13) Totsakan and Jill each improved their yards by planting rose bushes and geraniums. They bought their supplies from the same store. Totsakan spent $ on 9 rose bushes and 1 geraniums. Jill spent $0 on 3 rose bushes and 1 geranium. Find the cost of one rose bush and the cost of one geranium. 1) Heather and Perry each improved their yards by planting grass sod and geraniums. They bought their supplies from the same store. Heather spent $130 on ft² of grass sod and geraniums. Perry spent $115 on 1 ft² of grass sod and 5 geraniums. What is the cost of one ft² of grass sod and the cost of one geranium?

6 g vkbu0twau 5SCoGfBttwvaGrTey QLKLSCA.i a KAwlglc qrzi7gehqtsss trpepsoebr7vne3db.m I emqaadfe gw5iqtghh rimnjfyibnhidtge VAel1gdebArnan H1d.y -3- Worksheet by Kuta Software LLC Answers to Practice: Solving Systems of Equations (3 Different Methods) (ID: ) 1) (, 5) ) No solution 3) (3, 1) ) (0, ) 5) (, 3) ) (3, ) 7) ( 1, 3) ) ( 7, 3) 9) ( 9, 3) ) (, ) 11) senior citizen ticket: $, student ticket: $ 1) Van:, Bus: 35 13) rose bush: $, geranium: $ 1) ft² of grass sod: $5, geranium: $11

7 -1- s HKDutEam XSKojfCtfwqaHreeF QLsLSCB.f Z KAOllT KrziDgEhrtzsZ nryesoeryvjexdg.y TMKaydaeC pwli7tihy ZIWnGfjiHnniWtez QAUl3g0eQbirua G1.s Worksheet by Kuta Software LLC Da Vinci Design / Math 9 Practice: Solving Systems of Equations (3 Different Methods) Solve each system by substitution. ID: 3 Name Date 1) 9x 3y = 3x + y = 3 ) x + y = x + y = 1 3) x + y = 3x + y = 3 ) x + 7y = 5 x + y = 7 Solve each system by elimination. 5) 3x y = 1 x + 3y = ) 3x + y = 1 x + y = 7) x + 1y = 1 3x y = ) x + y = 1 1x + y = Solve each system by graphing. 9) y = 3 x 1 y = 7 3 x + ) y = 9 x y = x

8 -- y ukouytqax FSQoIfBtVwHaRreP flil5ci.b D AUlglx mroingzhvtlsr VrkeFsRearTvVeYdT.W E xma7dpek MwJi7tthc 0Iknaf9itniHtYey maplkgpesbbr9aa 51V.7 Worksheet by Kuta Software LLC 11) Jacob and Sumalee each improved their yards by planting daylilies and geraniums. They bought their supplies from the same store. Jacob spent $7 on 11 daylilies and geraniums. Sumalee spent $0 on daylilies and 1 geraniums. Find the cost of one daylily and the cost of one geranium. 1) Natalie and Anjali each improved their yards by planting hostas and shrubs. They bought their supplies from the same store. Natalie spent $ on hostas and 7 shrubs. Anjali spent $ on hostas and shrubs. Find the cost of one hosta and the cost of one shrub. 13) Jessica and Sarawong each improved their yards by planting daylilies and ornamental grass. They bought their supplies from the same store. Jessica spent $9 on daylilies and bunches of ornamental grass. Sarawong spent $ on daylilies and 5 bunches of ornamental grass. What is the cost of one daylily and the cost of one bunch of ornamental grass? 1) The school that Kayla goes to is selling tickets to the annual talent show. On the first day of ticket sales the school sold senior citizen tickets and 7 student tickets for a total of $11. The school took in $ on the second day by selling senior citizen tickets and 1 student ticket. What is the price each of one senior citizen ticket and one student ticket?

9 tkougtyaq 5SFoUfitlw1abrEeo KLLqCy.Z 0 ABltly 5rtiAgFhutIsY MreeWsWetrCvseLdJ.H V mmoa7dqe3 wiiitqhm cilnqf9iunviftee LAmlzgleWbVraaU g1g.l -3- Worksheet by Kuta Software LLC Answers to Practice: Solving Systems of Equations (3 Different Methods) (ID: 3) 1) No solution ) (, ) 3) ( 7, 3) ) (, 1) 5) (, ) ) ( 5, 1) 7) (, ) ) (0, 3) 9) (3, 1) ) (, 5) 11) daylily: $9, geranium: $ 1) hosta: $, shrub: $ 13) daylily: $9, bunch of ornamental grass: $ 1) senior citizen ticket: $3, student ticket: $1

10 -1- sk3uitaat 9SwoOf3tRwaOrReW 1LQL1Cy.m RA1lSl ZrLiUgthdtasb 7rmeysYeUrivWecdw. T SM7aLdbeA QwtiXtJhv ciynfhipnintet iaal7ggelbhrfab 1D.A Worksheet by Kuta Software LLC Da Vinci Design / Math 9 Practice: Solving Systems of Equations (3 Different Methods) Solve each system by substitution. ID: Name Date 1) 1x 3y = 7 7x + y = 3 ) x + y = 5x + y = 1 3) x y = x + y = ) x + 3y = 7 x + 7y = 5 Solve each system by elimination. 5) x y = 1x y = 1 ) 5x y = 1 x + 5y = 0 7) x y = 1x + 9y = 1 ) 3x 1y = 1 x y = Solve each system by graphing. 9) y = x 7 y = 9 ) y = 1 x 9 y = 1 x + 0 0

11 -- I rkouatjap KSRoFfvtawcaQrCek LDLdCa.V i NAblHl 1rvitghMthsG 1rxeCsReDrqvpeJdz.P U xmiahdpek NwqiDtAhP FICnVfSiLnLi5tSeM aaulggjejbhrnar v1i.l Worksheet by Kuta Software LLC 11) A boat traveled miles downstream and back. The trip downstream took hours. The trip back took 1 hours. What is the speed of the boat in still water? What is the speed of the current? 1) A boat traveled 1 miles downstream and back. The trip downstream took hours. The trip back took hours. What is the speed of the boat in still water? What is the speed of the current? 13) A plane traveled 00 miles to Tokyo and back. The trip there was with the wind. It took hours. The trip back was into the wind. The trip back took 0 hours. What is the speed of the plane in still air? What is the speed of the wind? 1) The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 1 vans and 11 buses with 737 students. High School B rented and filled vans and 5 buses with 31 students. Each van and each bus carried the same number of students. Find the number of students in each van and in each bus.

12 D YKCuotJaU QSo9fEtCwIaIreo 3LNLVCq.V i fabltlx urpisgnhztnsl Hr9eesnerPvtesdn.i C EM3aMd5eb Xwdi9tmhn BInmfKitnZietei 9ALlTgZembprZaH F1n.a -3- Worksheet by Kuta Software LLC Answers to Practice: Solving Systems of Equations (3 Different Methods) (ID: ) 1) No solution ) (, ) 3) (, ) ) (, 3) 5) (1, 1) ) (, ) 7) (3, ) ) (7, 0) 9) (, 9) ) No solution 11) boat: 15 mph, current: 5 mph 1) boat: 1 mph, current: 9 mph 13) plane: 0 mph, wind: 0 mph 1) Van: 11, Bus: 55

13 -1- YKbuItraY 1SoufAtlwVaerreV xllltct.i r kaolll IrxiWgyhotZsG rfeksveiryvyeodv.o N AMGaFdoeN ewyimt7hq zimnyf3ihn9ihtyed DAClQgcebbRraV 01x.a Worksheet by Kuta Software LLC Da Vinci Design / Math 9 Practice: Solving Systems of Equations (3 Different Methods) Solve each system by substitution. ID: 5 Name Date 1) x y = 9 5x + y = 5 ) x + y = 0 x + y = 3) 5x + y = 3 3x 5y = 15 ) 3x y = x y = Solve each system by elimination. 5) 9x 7y = 3x y = ) x + y = 5x + 5y = 0 7) 7x + y = 5 x + 5y = 0 ) 1x + 7y = 1 9x y = Solve each system by graphing. 9) y = 3 x y = 1 3 x 1 ) y = 1 x y = 9 x

14 -- x CKnutDa9 tswo5fjtgwearrvet flol5cd.x h daolzlh IrWiCgchPtWsd gryegsuejrhviefd7.e y om0andkeo 7w1iftjh9 libndfhixnsietwej faflgfedblriac F1L.X Worksheet by Kuta Software LLC 11) When you reverse the digits in a certain two-digit number you increase its value by 3. What is the number if the sum of its digits is? 1) Jasmine and Brenda are selling cheesecakes for a school fundraiser. Customers can buy pecan cheesecakes and apple cheesecakes. Jasmine sold pecan cheesecakes and apple cheesecakes for a total of $1. Brenda sold pecan cheesecakes and 7 apple cheesecakes for a total of $139. Find the cost each of one pecan cheesecake and one apple cheesecake. 13) A boat traveled 0 miles downstream and back. The trip downstream took hours. The trip back took hours. Find the speed of the boat in still water and the speed of the current. 1) A plane traveled 35 miles to Berlin and back. The trip there was with the wind. It took hours. The trip back was into the wind. The trip back took hours. Find the speed of the plane in still air and the speed of the wind.

15 z FKruLtSaK pspo5fjtpw3akrze3 hlulwct.9 a faelxlm hr0iagphzttsx XrDess9e0r7vnerdK.j Y LMgaYdAe7 Yw3iptKhG OIXnmf1iTnuiQtPeh fa3lygieubarbaj L1D.o -3- Worksheet by Kuta Software LLC Answers to Practice: Solving Systems of Equations (3 Different Methods) (ID: 5) 1) (, 5) ) (, ) 3) (0, 3) ) (, 0) 5) (, ) ) (, 0) 7) ( 5, ) ) (, 5) 9) (, 1) ) (, ) 11) 37 1) pecan cheesecake: $5, apple cheesecake: $17 13) boat: 15 mph, current: 5 mph 1) plane: mph, wind: mph