Chapter 6 Systems Linear Equations And Inequalities
Chapter 6 Resource MastersBothell, WA Chicago, IL Columbus, OH New York, NY
CONSUMABLE WORKBOOKS Many of the worksheets contained in the Chapter Resource Mastersbooklets are available as consumable workbooks in both English and Spanish.Study Guide and Intervention WorkbookHomework Practice 0-07-660292-6978-0-07-660291-9Spanish VersionHomework Practice Workbook0-07-660294-X978-0-07-660294-0Answers For Workbooks The answers for Chapter 6 of these workbooks can be found in theback of this Chapter Resource Masters booklet.ConnectED All of the materials found in this booklet are included for viewing, printing, and editing atconnected.mcgraw-hill.com.Spanish Assessment Masters (MHID: 0-07-660289-3, ISBN: 978-0-07-660289-6) These masterscontain a Spanish version of Chapter 6 Test Form 2A and Form 2C.connected.mcgraw-hill.comCopyright by The McGraw-Hill Companies, Inc.All rights reserved. The contents, or parts thereof, may bereproduced in print form for non-profit educational use withGlencoe Algebra 1, provided such reproductions bear copyrightnotice, but may not be reproduced in any form for any otherpurpose without the prior written consent of The McGraw-HillCompanies, Inc., including, but not limited to, network storageor transmission, or broadcast for distance learning.Send all inquiries to:McGraw-Hill Education8787 Orion PlaceColumbus, OH 43240ISBN: 978-0-07-660280-3MHID: 0-07-660280-XPrinted in the United States of America.1 2 3 4 5 6 7 8 9 DOH 16 15 14 13 12 11
ContentsTeacher’s Guide to Using the Chapter 6Resource Masters.ivSubstitutionStudy Guide and Intervention . 12Skills Practice . 14Practice . 15Word Problem Practice . 16Enrichment . 17Systems of InequalitiesStudy Guide and Intervention . 36Skills Practice . 38Practice . 39Word Problem Practice . 40Enrichment . 41Graphing Calculator . 42Spreadsheet . 43Student Recording Sheet . 45Rubric for Scoring Extended Response . 46Chapter 6 Quizzes 1 and 2 . 47Chapter 6 Quizzes 3 and 4 . 48Chapter 6 Mid-Chapter Test . 49Chapter 6 Vocabulary Test. 50Chapter 6 Test, Form 1 . 51Chapter 6 Test, Form 2A . 53Chapter 6 Test, Form 2B . 55Chapter 6 Test, Form 2C . 57Chapter 6 Test, Form 2D . 59Chapter 6 Test, Form 3 . 61Chapter 6 Extended-Response Test . 63Standardized Test Practice . 64Unit 2 Test. 67Lesson 6-3Answers . A1–A32Chapter ResourcesChapter 6 Student-Built Glossary. 1Chapter 6 Anticipation Guide (English) . 3Chapter 6 Anticipation Guide (Spanish) . 4Lesson 6-1Graphing Systems of EquationsStudy Guide and Intervention . 5Skills Practice . 7Practice . 8Word Problem Practice . 9Enrichment . 10Graphing Calculator Activity .11Lesson 6-2Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Lesson 6-6Elimination Using Addition and SubtractionStudy Guide and Intervention . 18Skills Practice . 20Practice . 21Word Problem Practice . 22Enrichment . 23Lesson 6-4Elimination Using MultipcationStudy Guide and Intervention . 24Skills Practice . 26Practice . 27Word Problem Practice . 28Enrichment . 29Lesson 6-5Applying Systems of Linear EquationsStudy Guide and Intervention . 30Skills Practice . 32Practice . 33Word Problem Practice . 34Enrichment . 35iii
Teacher’s Guide to Using theChapter 6 Resource MastersThe Chapter 6 Resource Masters includes the core materials needed for Chapter 6. Thesematerials include worksheets, extensions, and assessment options. The answers for thesepages appear at the back of this booklet.All of the materials found in this booklet are included for viewing, printing, andediting at connectED.mcgraw-hill.com.Chapter ResourcesStudent-Built Glossary (pages 1–2) Thesemasters are a student study tool thatpresents up to twenty of the key vocabularyterms from the chapter. Students are torecord definitions and/or examples for eachterm. You may suggest that studentshighlight or star the terms with which theyare not familiar. Give this to students beforebeginning Lesson 6-1. Encourage them toadd these pages to their mathematics studynotebooks. Remind them to complete theappropriate words as they study each lesson.Lesson ResourcesStudy Guide and Intervention Thesemasters provide vocabulary, key concepts,additional worked-out examples and GuidedPractice exercises to use as a reteachingactivity. It can also be used in conjunctionwith the Student Edition as an instructionaltool for students who have been absent.Practice This master closely follows thetypes of problems found in the Exercisessection of the Student Edition and includesword problems. Use as an additionalpractice option or as homework for secondday teaching of the lesson.Word Problem Practice This masterincludes additional practice in solving wordproblems that apply the concepts of thelesson. Use as an additional practice or ashomework for second-day teaching of thelesson.Enrichment These activities may extendthe concepts of the lesson, offer a historicalor multicultural look at the concepts, orwiden students’ perspectives on themathematics they are learning. They arewritten for use with all levels of students.Graphing Calculator, TI-Nspire, orSpreadsheet ActivitiesThese activities present ways in whichtechnology can be used with the concepts insome lessons of this chapter. Use as analternative approach to some concepts or asan integral part of your lesson presentation.ivCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Anticipation Guide (pages 3–4) Thismaster, presented in both English andSpanish, is a survey used before beginningthe chapter to pinpoint what students mayor may not know about the concepts in thechapter. Students will revisit this surveyafter they complete the chapter to see iftheir perceptions have changed.Skills Practice This master focuses moreon the computational nature of the lesson.Use as an additional practice option or ashomework for second-day teaching of thelesson.
Assessment OptionsThe assessment masters in the Chapter 6Resource Masters offer a wide range ofassessment tools for formative (monitoring)assessment and summative (final)assessment.Student Recording Sheet This master corresponds with the standardized testpractice at the end of the chapter.Extended Response Rubric This masterprovides information for teachers andstudents on how to assess performance onopen-ended questions.Quizzes Four free-response quizzes offerassessment at appropriate intervals in thechapter.Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Mid-Chapter Test This 1-page testprovides an option to assess the first half ofthe chapter. It parallels the timing of theMid-Chapter Quiz in the Student Editionand includes both multiple-choice andfree-response questions.Vocabulary Test This test is suitable forall students. It includes a list of vocabularywords and 9 questions to assess students’knowledge of those words. This can also beused in conjunction with one of the leveledchapter tests.Leveled Chapter Tests Form 1 contains multiple-choicequestions and is intended for use withbelow grade level students. Forms 2A and 2B contain multiplechoice questions aimed at on grade levelstudents. These tests are similar informat to offer comparable testingsituations. Forms 2C and 2D contain freeresponse questions aimed at on gradelevel students. These tests are similarin format to offer comparable testingsituations. Form 3 is a free-response test for usewith above grade level students.All of the above mentioned tests include afree-response Bonus question.Extended-Response Test Performanceassessment tasks are suitable for allstudents. Sample answers and a scoringrubric are included for evaluation.Standardized Test Practice These threepages are cumulative in nature. It includesthree parts: multiple-choice questions withbubble-in answer format, griddablequestions with answer grids, and shortanswer free-response questions.Answers The answers for the Anticipation Guideand Lesson Resources are provided asreduced pages. Full-size answer keys are provided forthe assessment masters.v
NAMEDATE6PERIODThis is an alphabetical list of the key vocabulary terms you will learn in Chapter 6.As you study the chapter, complete each term’s definition or description.Remember to add the page number where you found the term. Add these pages toyour Algebra Study Notebook to review vocabulary at the end of the chapter.Vocabulary TermFoundon shuhnCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, �TOO·shuhnsystem of equationssystem of inequalitiesChapter 61Glencoe Algebra 1Chapter ResourcesStudent-Built Glossary
NAME6DATEPERIODAnticipation GuideStep 1Before you begin Chapter 6 Read each statement. Decide whether you Agree (A) or Disagree (D) with the statement. Write A or D in the first column OR if you are not sure whether you agree ordisagree, write NS (Not Sure).STEP 1A, D, or NSSTEP 2A or DStatement1. A solution of a system of equations is any ordered pair thatsatisfies one of the equations2. A system of equations of parallel lines will have no solutions.3. A system of equations of two perpendicular lines will haveinfinitely many solutions.4. It is not possible to have exactly two solutions to a system oflinear equationsCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.5. The most accurate way to solve a system of equations is tograph the equations to see where they intersect.6. To solve a system of equations, such as 2x - y 21 and3y 2x - 6, by substitution, solve one of the equations forone variable and substitute the result into the other equation.7. When solving a system of equations, a result that is a truestatement, such as -5 -5, means the equations do notshare a common solution.8. Adding the equations 3x - 4y 8 and 2x 4y 7 resultsin a 0 coefficient for y.9. The equation 7x - 2y 12 can be multiplied by 2 so that thecoefficient of y is -4.10. The result of multiplying -7x - 3y 11 by -3 is-1x 9y 11.Step 2After you complete Chapter 6 Reread each statement and complete the last column by entering an A or a D. Did any of your opinions about the statements change from the first column? For those statements that you mark with a D, use a piece of paper to write anexample of why you disagree.Chapter 63Glencoe Algebra 1Chapter ResourcesSolving Systems of Linear Equations
NOMBRE6FECHAPERÍODOEjercicios preparatoriosResuelve sistemas de ecuaciones linealesPaso 1Antes de comenzar el Capítulo 6 Lee cada enunciado. Decide si estás de acuerdo (A) o en desacuerdo (D) con el enunciado. Escribe A o D en la primera columna O si no estás seguro(a) de la respuesta,escribe NS (No estoy seguro(a)).PASO 1A, D o NSPASO 2AoDEnunciado1. Una solución de un sistema de ecuaciones es cualquier parordenado que satisface una de las ecuaciones2. Un sistema de ecuaciones de rectas paralelas no tendrá soluciones.3. Un sistema de ecuaciones de dos rectas perpendicularestendrá un número infinito de soluciones.4. No es posible tener exactamente dos soluciones para unsistema de ecuaciones lineales.5. La forma más precisa de resolver un sistema de ecuaciones esgraficar las ecuaciones y ver dónde se intersecan.7. Cuando se resuelve un sistema de ecuaciones, un resultadoque es un enunciado verdadero, como -5 -5, significa quelas ecuaciones no comparten una solución.8. El sumar las ecuaciones 3x - 4y 8 y 2x 4y 7 resulta en uncoeficiente de 0 para y.9. La ecuación 7x - 2y 12 se puede multiplicar por 2, de modoque el coeficiente de y es -4.10. El resultado de multiplicar -7x - 3y 11 por -3 es -1x 9y 11.Paso 2Después de completar el Capítulo 6 Vuelve a leer cada enunciado y completa la última columna con una A o una D. ¿Cambió cualquiera de tus opiniones sobre los enunciados de la primera columna? En una hoja de papel aparte, escribe un ejemplo de por qué estás en desacuerdo con losenunciados que marcaste con una D.Capítulo 64Álgebra 1 de GlencoeCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.6. Para resolver un sistema de ecuaciones, como 2x - y 21 y3y 2x - 6, por sustitución, despeja una variable en una dela ecuaciones y reemplaza el resultado en la otra ecuación.
NAME6-1DATEPERIODStudy Guide and InterventionGraphing Systems of EquationsGraph of a Systemintersecting linessame lineOparallel linesyyyxOxOxNumber of Solutionsexactly one solutioninfinitely many solutionsno solutionTerminologyconsistent andindependentconsistent anddependentinconsistentExampleyUse the graph at the right to determinewhether each system is consistent or inconsistent andif it is independent or dependent.Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Lesson 6-1Possible Number of Solutions Two or more linear equations involving the samevariables form a system of equations. A solution of the system of equations is an orderedpair of numbers that satisfies both equations. The table below summarizes informationabout systems of linear equations.y x 1a. y -x 2y -x - 1y -x 2y x 1xOSince the graphs of y -x 2 and y x 1 intersect,there is one solution. Therefore, the system is consistent3x 3y -3and independent.b. y -x 23x 3y -3Since the graphs of y -x 2 and 3x 3y -3 areparallel, there are no solutions. Therefore, the system is inconsistent.c. 3x 3y -3y -x - 1Since the graphs of 3x 3y -3 and y -x - 1 coincide,there are infinitely many solutions. Therefore, the system is consistent and dependent.ExercisesyUse the graph at the right to determine whether eachsystem is consistent or inconsistent and if it isindependent or dependent.1. y -x - 3y x-12. 2x 2y -6y -x - 33x y 32x 2y 4Ox2x 2y -6y x-1y -x - 33. y -x - 32x 2y 4Chapter 64. 2x 2y -63x y 35Glencoe Algebra 1
NAMEDATE6-1PERIODStudy Guide and Intervention (continued)Graphing Systems of EquationsSolve by Graphing One method of solving a system of equations is to graph theequations on the same coordinate plane.ExampleGraph each system and determine the number of solutions that ithas. If it has one solution, name it.ya. x y 2x-y 4The graphs intersect. Therefore, there is one solution. Thepoint (3, -1) seems to lie on both lines. Check this estimateby replacing x with 3 and y with -1 in each equation.x y 23 (-1) 2 x-y 43 - (-1) 3 1 or 4 The solution is (3, -1).b. y 2x 12y 4x 2The graphs coincide. Therefore there are infinitelymany solutions.x y 2Ox(3, –1)x-y 4yy 2x 12y 4x 2xOExercises1. y -213. y x2. x 23x - y -122x y 1yxOx y 3yyxOxO5. 3x 2y 63x 2y -44. 2x y 62x - y -2yyChapter 6yxOO6. 2y -4x 4y -2x 2Oxx6Glencoe Algebra 1Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Graph each system and determine the number of solutions it has. If it has onesolution, name it.
NAMEDATE6-1PERIODSkills PracticeUse the graph at the right to determine whethereach system is consistent or inconsistent and if it isindependent or dependent.yy x 4x - y -41. y x - 12x - 2y 22. x - y -4y -x 1x0y x 4y -x 1y x-13. y x 42x - 2y 24. y 2x - 32x - 2y 2y 2x - 3Graph each system and determine the number of solutions that it has.If it has one solution, name it.5. 2x - y 1y -36. x 12x y 4yCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.yyxOxO9. x 3y -3x - 3y -38. y x 2x - y -211. x - y 3x1y - x 2yyxxOChapter 63y 6x - 62yx013. y 2x 312. x 2y 4x - 2y 3010. y - x -1x y 3yOxxOyy07. 3x y -33x y 37OxGlencoe Algebra 1Lesson 6-1Graphing Systems of Equations
NAME6-1DATEPERIODPracticeGraphing Systems of EquationsUse the graph at the right to determine whethereach system is consistent or inconsistent andif it is independent or dependent.yx 3y 32x - y -3x y 31. x y 3x y -32. 2x - y -34x - 2y -63. x 3y 3x y -3x04x - 2y -6x y -34. x 3y 32x - y -3Graph each system and determine the number of solutions that it has. If it hasone solution, name it.5. 3x - y -23x - y 06. y 2x - 34x 2y 6yyyxOO7. x 2y 33x - y -5xxa. Graph the system of equations y 0.5x 20 andy 1.5x to represent the situation.403020155040252015105c. How many CDs and videos did the store sell in thefirst week?08CD and Video Sales30b. Graph the system of equations.Chapter 65 10 15 20 25 30 35 40 45Sales ( )35Video Sales ( )a. Write a system of equations torepresent the situation.2510b. How many treats does Nick need to sell per week tobreak even?9. SALES A used book store also started selling usedCDs and videos. In the first week, the store sold 40used CDs and videos, at 4.00 per CD and 6.00 pervideo. The sales for both CDs and videos totaled 180.00Dog Treats35Cost ( )8. BUSINESS Nick plans to start a home-based businessproducing and selling gourmet dog treats. He figures itwill cost 20 in operating costs per week plus 0.50 toproduce each treat. He plans to sell each treat for 1.50.5 10 15 20 25 30 35 40 45CD Sales ( )Glencoe Algebra 1Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.0
NAMEDATE6-1PERIODWord Problem Practice1. BUSINESS The widget factory willsell a total of y widgets after x daysaccording to the equation y 200x 300.The gadget factory will sell y gadgetsafter x days according to the equationy 200x 100. Look at the graph of thesystem of equations and determinewhether it has no solution, one solution,or infinitely many solutions.900y4. AVIATION Two planes are in flight neara local airport. One plane is at analtitude of 1000 meters and is ascendingat a rate of 400 meters per minute. Thesecond plane is at an altitude of5900 meters and is descending at a rateof 300 meters per minute.a. Write a system of equations thatrepresents the progress of each planey 200x 300 Widgets800Items sold700600500400y 200x 100 Gadgetsb. Make a graph that represents theprogress of each plane.300200100123 4Days5y6 x2. ARCHITECTURE An office building hastwo elevators. One elevator starts out onthe 4th floor, 35 feet above the ground,and is descending at a rate of 2.2 feet persecond. The other elevator starts out atground level and is rising at a rate of1.7 feet per second. Write a system ofequations to represent the situation.Altitude (m)Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.0x0Time (min.)3. FITNESS Olivia and her brother Williamhad a bicycle race. Olivia rode at a speedof 20 feet per second while William rodeat a speed of 15 feet per second. To befair, Olivia decided to give William a150-foot head start. The race ended in atie. How far away was the finish linefrom where Olivia started?Chapter 69Glencoe Algebra 1Lesson 6-1Graphing Systems of Equations
NAMEDATE6-1PERIODEnrichmentGraphing a TripdThe distance formula, d rt, is used to solve many types ofproblems. If you graph an equation such as d 50t, the graph isa model for a car going at 50 mph. The time the car travels is t;the distance in miles the car covers is d. The slope of the line isthe speed.Suppose you drive to a nearby town and return. You average50 mph on the trip out but only 25 mph on the trip home. Theround trip takes 5 hours. How far away is the town?The graph at the right represents your trip. Notice that the returntrip is shown with a negative slope because you are driving in theopposite direction.slope is 50slope is –25502OtSolve each problem.1. Estimate the answer to the problem in the above example. Abouthow far away is the town?Graph each trip and solve the problem.d100O3. You drive to a town 100 miles away.On the trip out you average 25 mph.On the trip back you average 50 mph.How many hours do you spend driving?d5050Chapter 6t4. You drive at an average speed of 50 mphto a discount shopping plaza, spend2 hours shopping, and then return at anaverage speed of 25 mph. The entire triptakes 8 hours. How far away is theshopping plaza?dO12tO102tGlencoe Algebra 1Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.2. An airplane has enough fuel for 3 hours ofsafe flying. On the trip out the pilot averages200 mph flying against a headwind. On thetrip back, the pilot averages 250 mph. Howlong a trip out can the pilot make?
NAMEDATE6-1PERIODGraphing Calculator ActivitySolution to a System of Linear EquationsExampleLesson 6-1A graphing calculator can be used to solve a system of linear equations graphically. Thesolution of a system of linear equations can be found by using the TRACE feature or byusing the intersect command under the CALC menu.Solve each system of linear equations.a. x y 0x - y -4Using TRACE: Solve each equation for y and enter each equationinto Y . Then graph using Zoom 8: ZInteger. Use TRACE to findthe solution. 4 ZOOM 6ENTERKeystrokes: Y (–)ZOOM8.TRACEENTER[-47, 47] scl:10 by [-31, 31]scl:10The solution is (-2, 2).b. 2x y 44x 3y 3Using CALC: Solve each equation for y, enter each into theCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.calculator, and graph. Use CALC to determine the solution.Keystrokes: 1Y (–) 426ZOOM2nd[CALC] 5ENTERTo change the x-value to a fraction, pressMATHENTERENTER(–)(ENTER4 3ENTER2nd)ENTER.[QUIT][-10, 10] scl:1 by [-10, 10]scl:1.(2)9, -5 .The solution is (4.5, -5) or ExercisesSolve each system of linear equations.1. y 25x 4y 182. y -x 3y x 13. x y -12x - y -84. -3x y 10-x 2y 05. -4x 3y 107x y 206. 5x 3y 11x - 5y 57. 3x - 2y -4-4x 3y 58. 3x 2y 4-6x - 4y -89. 4x - 5y 06x - 5y 10Chapter 6010 018 ALG1 A CRM C06 CR 660280.indd 1111Glencoe Algebra 1PDF 2nd12/24/10 7:07 AM
NAME6-2DATEPERIODStudy Guide and InterventionSubstitutionSolve by SubstitutionOne method of solving systems of equations is substitution.Example 1Use substitution tosolve the system of equations.y 2x4x - y -4Example 2Solve for one variable,then substitute.x 3y 72x - 4y -6Substitute 2x for y in the secondequation.4x - y -4Second equation4x - 2x -4y 2x2x -4Combine like terms.x -2Divide each side by 2Solve the first equation for x since the coefficientof x is 1.x 3y 7First equationx 3y - 3y 7 - 3ySubtract 3y from each side.x 7 - 3ySimplify.Find the value of y by substituting 7 - 3y for xin the second equation.2x - 4y -6Second equation2(7 - 3y) - 4y -6x 7 - 3y14 - 6y - 4y -6Distributive Property14 - 10y -6Combine like terms.14 - 10y - 14 -6 - 14 Subtract 14 from each side.-10y -20Simplify.y 2Divide each side by -10and simplify.Use y 2x to find the value of y.y 2xFirst equationy 2(-2)x -2y -4Simplify.The solution is (-2, -4).Use y 2 to find the value of x.x 7 - 3yx 7 - 3(2)x 1The solution is (1, 2).ExercisesUse substitution to solve each system of equations.1. y 4x3x - y 12. x 2yy x-23. x 2y - 3x 2y 44. x - 2y -13y x 45. x - 4y 12x - 8y 26. x 2y 03x 4y 47. 2b 6a - 143a - b 78. x y 162y -2x 29. y -x 32y 2x 410. x 2y0.25x 0.5y 10Chapter 611. x - 2y -5x 2y -11212. -0.2x y 0.50.4x y 1.1Glencoe Algebra 1Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.and simplify.
NAME6-2DATEPERIODStudy Guide and Intervention (continued)SubstitutionSolve Real-World ProblemsSubstitution can also be used to solve real-worldproblems involving systems of equations. It may be helpful to use tables, charts, diagrams,or graphs to help you organize data.ExampleCHEMISTRY How much of a 10% saline solution should be mixedwith a 20% saline solution to obtain 1000 milliliters of a 12% saline solution?Let s the number of milliliters of 10% saline solution.Let t the number of milliliters of 20% saline solution.Use a table to organize the information.Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Milliliters of saline20% saline12% salinest10000.10 s0.20 t0.12(1000)Write a system of equations.s t 10000.10s 0.20t 0.12(1000)Use substitution to solve this system.s t 1000s 1000 - t0.10s 0.20t 0.12(1000)0.10(1000 - t) 0.20t 0.12(1000)100 - 0.10t 0.20t 0.12(1000)100 0.10t 0.12(1000)0.10t 200.10t20 0.100.10Lesson 6-210% salineTotal millilitersFirst equationSolve for s.Second equations 1000 - tDistributive PropertyCombine like terms.Simplify.Divide each side by 0.10.t 200Simplify.s t 1000First equations 200 1000t 200s 800Solve for s.800 milliliters of 10% solution and 200 milliliters of 20% solution should be used.Exercises1. SPORTS At the end of the 2007–2008 football season, 38 Super Bowl games had beenplayed with the current two football leagues, the American Football Conference (AFC)and the National Football Conference (NFC). The NFC won two more games than theAFC. How many games did each conference win?2. CHEMISTRY A lab needs to make 100 gallons of an 18% acid solution by mixing a 12%acid solution with a 20% solution. How many gallons of each solution are needed?3. GEOMETRY The perimeter of a triangle is 24 inches. The longest side is 4 inches longerthan the shortest side, and the shortest side is three-fourths the length of the middleside. Find the length of each side of the triangle.Chapter 613Glencoe Algebra 1
NAME6-2DATEPERIODSkills PracticeSubstitutionUse substitution to solve each system of equations.1. y 4xx y 52. y 2xx 3y -143. y 3x2x y 154. x -4y3x 2y 205. y x - 1x y 36. x y - 7x 8y 27. y 4x - 1y 2x - 58. y 3x 85x 2y 59. 2x - 3y 21y 3-x10. y 5x - 84x 3y 3312. x 5y 43x 15y -113. 3x - y 42x - 3y -914. x 4y 82x - 5y 2915. x - 5y 102x - 10y 2016. 5x - 2y 142x - y 517. 2x 5y 38x - 3y -318. x - 4y 273x y -2319. 2x 2y 7x - 2y -120. 2.5x y -23x 2y 0Chapter 614Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.11. x 2y 133x - 5y 6Glencoe Algebra 1
NAME6-2DATEPERIODPracticeSubstitution1. y 6x2x 3y -202. x 3y3x - 5y 123. x 2y 7x y 44. y 2x - 2y x 25. y 2x 62x - y 26. 3x y 12y -x - 27. x 2y 13- 2x - 3y -188. x - 2y 34x - 8y 129. x - 5y 362x y -1610. 2x - 3y -24x 6y 1811. x 14y 842x - 7y -712. 0.3x - 0.2y 0.5x - 2y -513. 0.5x 4y -114. 3x - 2y 11115. x 2y 121x- y 42x 2.5y 3.5116. x-y 3317. 4x - 5y -7Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.2x y 25y 5x2x - 2y 618. x 3y -42x 6y 519. EMPLOYMENT Kenisha sells athletic shoes part-time at a department store. She canearn either 500 per month plus a 4% commission on her total sales, or 400 per monthplus a 5% commission on total sales.a. Write a system of equations to represent the situation.b. What is the total price of the athletic shoes Kenisha needs to sell to earn the sameincome from each pay scale?c. Which is the better offer?20. MOVIE TICKETS Tickets to a movie cost 7.25 for adults and 5.50 for students. Agroup of friends purchased 8 tickets for 52.75.a. Write a system of equations to represent the situation.b. How many adult tickets and student tickets were purchased?Chapter 615Glencoe Algebra 1Lesson 6-2Use substitution to solve each system of equations.
NAME6-2DATEPERIODWord Problem PracticeSubstitution1. BUSINESS Mr. Randolph finds that thesupply and demand for gasoline at hisstation are generally given by thefollowing equations.x - y -2x y 104. POPULATION Sanjay is researchingpopulation trends in South America. Hefound that the population of Ecuador toincreased by 1,000,000 and thepopulation of Chile to increased by600,000 from 2004 to 2009. The tabledisplays the information he found.Use substitution to find the equilibriumpoint where
Solving Systems of Linear Equations STEP 1 A, D, or NS Statement STEP 2 A or D 1. A solution of a system of equations is any ordered pair that satisfies one of the equations 2. A system of equations of parallel lines will have no solutions. 3. A system of equations of two pe
KEY: system of linear equations solution of a system of linear equations solving systems of linear equations by graphing solving systems of linear equations NOT: Example 2 3. 2x 2y 2 7x y 9 a. (1, 9) c. (0, 9) b. (2, 3) d. (1, 2) ANS: D REF: Algebra 1 Sec. 5.1 KEY: system of linear equations solution of a system of .
EQUATIONS AND INEQUALITIES Golden Rule of Equations: "What you do to one side, you do to the other side too" Linear Equations Quadratic Equations Simultaneous Linear Equations Word Problems Literal Equations Linear Inequalities 1 LINEAR EQUATIONS E.g. Solve the following equations: (a) (b) 2s 3 11 4 2 8 2 11 3 s
Part One: Heir of Ash Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26 Chapter 27 Chapter 28 Chapter 29 Chapter 30 .
These two linear equations model the situation: 12s 24l 780 s l 20 These two equations form a system of linear equations in two variables, sand l. A system of linear equations is often referred to as a linear system. A solution of a linear system is a pair of values of s and l that satisfy both equations.
Section 5.1 Solving Systems of Linear Equations by Graphing 237 Solving Systems of Linear Equations by Graphing The solution of a system of linear equations is the point of intersection of the graphs of the equations. CCore ore CConceptoncept Solving a System of Linear Equations by Graphing Step
TO KILL A MOCKINGBIRD. Contents Dedication Epigraph Part One Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Part Two Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18. Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26
Unit 12: Media Lesson Section 12.1: Systems of Linear Equations Definitions Two linear equations that relate the same two variables are called a system of linear equations. A solution to a system of linear equations is an ordered pair that satisfies both equations. Example 1: Verify that the point (5, 4) is a soluti
Linear and quadratic equations CONTENTS Examples: Solving linear equations 2 Questions on solving linear equations using a CAS calculator . Year 11 Linear and quadratic equations Page 10 of 12 Answers Linear equation questions Quadratic equation questions Equation graphing question
