I Can I Can A.CED.3, A.REI.6, MP.3, MP

Page 10Algebra I Unit 2 Linear RelationshipsChapter 6 Systems of Linear Equations and InequalitiesLesson 6-1 Graphing Systems of EquationsObjectives: CCSS: I can determine the number of solutions a system of linear equations has, ifany. I can solve systems of linear equations by graphing. A.CED.3, A.REI.6, MP.3, MP.8Example 1: Number of SolutionsUse the graph to determine whether each system is consistent or inconsistent and if itis independent or dependent.a. ? oinconsistent Consistentindependent b.

Guided Practice 1: Number of SolutionsUse the graph to determine whether each system is consistent or inconsistent and if itis independent or tentb.Example 2: Solve by GraphingGraph each system and determine the number of solutions that ithas. If it has one solution, name it.nxtba.,-infinitely 1/840--0,37ply .8#-43 1,20many-4y 4y -412--12(QD 4-4y )-8 -44# /(-20 /9 5"5)

b.'e I i Izrgwioe: :9Zy x.-zrunz- z zy k .- -11Guided Practice 2: Solve by GraphingGraph each system and determine the number of solutions that ithas. If it has one solution, name it.y x50101%5,1 )-2 y t3a. . a -2:F3 y -2 -3tryorpgP816/-1 b.#y:FLo#3µ5i9#421-521-7 .Real-World Example 3: Write and Solve a System of EquationsAlex rode 20 miles last week and plans to ride 35 miles per week. David rode 50 miles last weekand plans to ride 25 miles per week. Predict the week in which Alex and David will have riddenthe same number of miles.

Guided Practice 3: Write and Solve a System of EquationsJoe and Josh want to buy a video game. Joe has 14 and saves 10 a week. Josh has 26 andsaves 7 a week. In how many weeks will they have the same amount?

Lesson 6-2 Substitution Objectives:I can solve systems of equations by using substitution.I can solve real-world problems involving systems of equations by usingsubstitution. CCSS: A.CED.3, A.REI.6, MP.2Example 1: Solve a system by SubstitutionUse substitution to solve the system of equations. l 12Txpy -2 1-(-4 12) 2y -467*2,ZOTR---2 12 2-iz-Guided Practice 1: Solve a system by SubstitutionUse substitution to solve the system of equations.11 11 31-37 10y -n2 5-(3 10) -1F2 15 50 -117 50 -1-50 7 -50-51F-9 10@

Example 2: Solve and Then SubstituteUse substitution to solve the system of equations.Oxus( zy-- 29 2y#m3)w2C 3)5y 24 -36-3x@,y 3 y@*9 51 24legHy-3--9 24to 9IGuided Practice 2: Solve and Then SubstituteUse substitution to solve the system of equations.# 3 3-y 3X -134 5-(3 -13) 114 15 -165 1)19 7855't'ts19 -76T9T9@y 3C 4) 13-1312-Example 3: No Solution or Infinitely Many SolutionsUse substitution to solve the system of equations. 2 29 82#2y -4-No8 -4solutionGuided Practice 3: No Solution or Infinitely Many SolutionsUse substitution to solve the system of equations.a.[D Zx-(2 -3) 8 3482 Noa(solution b.)*-2 -6g-8 -2plymany

Real-World Example 4: Write and Solve a System of EquationsA nature center charges 35.25 for a yearly membership and 6.25 for a single admission. Lastweek it sold a combined total of 50 yearly memberships and single admissions for 660.50. Howmany memberships and how many single admissions were sold?ysingle admissionX yearlyy membershipy-Xty- 5035.254 6.25 2660.5055.050X 35.25g 6.25Guided Practice 4: Write and Solve a System of Equations* zt (50-Wg)Red 's worbdan.esFiyanraiswosrerdie,35.25g -1312.50-6.255-660.5Xty 32CCSS:F29y lZ5.4 3z6.4 3zLesson 6-3 Elimination Using Addition and Subtraction -1312.5 66;29g2-95-3485 40XtObjectives:-1660.50As of 2009, the New York Yankees and the Cincinnati Reds together had won a total of 32 WorldSeries. The Yankees had won 5.4 times as many as the Reds. How many World Series had eachteam won?-12-12*3850J I can solve systems of equations by using elimination with addition. I can solve systems of equations by using elimination with subtraction A.CED.2, A.REI.6, MP.7*54 27

Example 1: Elimination Using AdditionUse elimination to solve the system of equations.\so3 -6453 183 9900 1890 y2 3%6 6-@4yt3( 6) 366-4g 228 22(--72-%@Guided Practice 1: Elimination Using AdditionUse elimination to solve the system of equations.\3 1818 oExample 2: Write and Solve a System of EquationsFour times one number minus three times another number is 12. Two times the first numberadded to three times the second number is 6. Find the numbers.4X3y- 1243)zxth.IE#oItt33EIotuGuided Practice 2: Write and Solve a System of EquationsThe sum of two numbers is –10. Negative three times the first number minus the second numberequals 2. Find the numbers.to * E*y t5Ii oXty -Standardized Test Example 3:Use elimination to solve the system of equations.

4 25-28(§f--%xt3y #15y 4 24 24810@y 24 x z A., B. C. D.Guided Practice 3: Use elimination to solve the system of equations.&b-7c 8bt3c L F.@c 4c 4-8bF3 3,.86 14 4A G.8bt3tI) H11 js H. b 13g J.Real-World Example 4: Write and Solve a System of EquationsA hardware store earned 956.50 from renting ladders and power tools last week. The storecharged customers for a total of 36 days for ladders and 85 days for power tools. This week thestore charged 36 days for ladders, 70 days for power tools, and earned 829. How much does thestore charge per day for ladders and for power tools?956,50 362 8513Lptlapdrdfrepowerpntoul -956.5 36szq- 362 703 @zq Ltssp-36L-829FOP t5 gp75p 8'50829 361 595Guided Practice 4: Write and Solve a System of Equations36[234 LTamera and Addie are throwing a birthday party for their friend. Tamera invited 5 fewer friendsthan Addie. Together they invited 47 guests. How many guests did each girl invite?A T Addie 's friends's friendsTameraAttA 7018 36L 47#6.50 262- 5T-2A z6T 5,zu-52-26T -21

Lesson 6-4 Elimination Using MultiplicationI can solve systems of equations by using elimination with multiplication. I can solve real-world problems involving systems of equations. .REI.5, A.REI.6, MP.1AObjectives: CCSS:Example 1: Multiply One Equation to Eliminate a VariableII. y@18 5-23ZUse elimination to solve the system of equations.(*yx I IYa --(9)ty 23-189-Guided Practice 1: Multiply One Equation to Eliminate a VariableUse elimination to solve the system of equations.(# 29k z( 2)-26F n roizgI - 8r3r-2g--129 -4Example 2: Multiply Both Equations to Eliminate a VariableUse elimination to solve the system of equations.M-4020 15)5((W)3]ok-.#-29@-69isy Z9 -6 zq.29Ifhe4fDt3y 8 35 #35-12,5y@5

Guided Practice 2: Multiply Both Equations to Eliminate a VariableUse elimination to solve the system of equations.#53I-3562EITFEK.ca#H oy X 34 -0DeftReal-World Example 3: Solve a System of EquationsA fishing boat travels 10 miles down-stream in 30 minutes. The return trip takes the boat 40minutes. Find the rate in miles per hour of the boat in still water.4 1.5 1Boatspeed-dO-tzxtlzyjzycor 2yxx-2d X-l7.5m@DTj-BIaoIspeedC4-lxt.lD1.sGuided Practice 3: Solve a System of EquationsA canoeist travels 4 miles downstream in 1 hour. The return trip takes the canoeist 1.5 hours. Findthe rate of the boat in still water.y current.5yspeed'6 1.5 1 .5yx 3'rsmeh4,5155 151Lesson 6-5 Applying Systems of Linear EquationsObjectives: CCSS:I can determine the best method for solving systems of equations. I can apply systems of equations. .REI.6, MP.2, MP.4A

Example 1: Choose the Best MethodDetermine the best method to solve the system of equations. Then solve the system.#z@-6*-464 4 34-4 (\-2 313 23--H2y 122 9 23-IfTyq--q #Guided Practice 1: Choose the Best MethodDetermine the best method to solve the system of equations. Then solve the system.FAIE ka.in.is#y 9-7x 7 7 72t7y 9@7yj@ijIni5x 'b. ' y 5x#-T'3 2y 5(asy l5(5 -17) 53 10 -34 513 -34 5 34 34l3 39T3I #3)--yd1717

Real-World Example 2: Apply Systems of Linear EquationsAce Car Rental rents a car for 45O andO and 0.25 per mile. Star Car Rental rents a car for 35 0.30 per mile. How many miles would a driver need to drive before the cost of renting a car atAce Car Rental and renting a car at Star Car Rental were the same?- y hfiogkf25 45.Y 30 35.25 45.30 t}s5 .28xt.IE?fsxX 2oomi@T tofalhwrsT 3Wt50-.-25 35-Guided Practice 2: Apply Systems of Linear EquationsJared has volunteered 50 hours and plans to volunteer 3 hours in each coming week. Maddie is anew volunteer who plans to volunteer 5 hours each week. Write and solve a system of equationsto find how long it will be before they will have volunteered the same number of hours.WeeksWeT 2w 505W5w 3w 5ow 2Ee 3W--3WLesson 6-6 Systems of InequalitiesI can solve systems of linear inequalities by graphing. I can apply systems of linear inequalities. .REI.12, MP.1, MP.6AObjectives: CCSS:Tha.1( testpt3lineK) 4"shading .t.gg#Gq@Dashed/S0lidExample 1: Solve by graphingSolve the system of inequalities by graphing.B ,test #0 20 )0 202-QD(002-3 2True-3!True !.

:intradaylot - Guided Practice 1: Solve by graphingSolve the system of inequalities by graphing.Aa.0 3HeFalseuDto0EImeZCO-4b.-2 - yzzx, Example 2: No SolutionA-2 -2y 2-10 4)9L 010 )PtTestATrue0 0 -1 1171710,0 )TestDBa"'.o Test d.3( 0 )02 2Guided Practice 2: No SolutionSolve the system of inequalities by graphing.B !. .-2False !,NO .02-30 1False.a.( 010 )Pt- -2 40 -101 .Solve the system of inequalities by graphing.13Ibm.41mA gowtim

t -7*7%54,1/30zwaiflike d Example 3: Whole-Number SolutionsA college service organization requires that its members maintain at least a 3.0 grade pointaverage and volunteer at least 10 hours a week.a. Define the variables and write a system ofinequalities to represent this situation. Then graphthe system.b. Name one possible solution.L 4,11)Guided Practice 3: Whole-Number Solutions

The Theater Club is selling shirts. They have only enough supplies to print 120 shirts. They willsell sweatshirts for 22 and T-shirts for 15, with a goal of at least 2000 in sales.a. Define the variables, and write a system of inequalities to represent this situation. Thengraph the system.1-b. Name one possible solution.c. Is (45,30) a solution? Explain.

Lesson 6-3 Elimination Using Addition and Subtraction Objectives: I can solve systems of equations by using elimination with addition. I can solve systems of equations by using elimination with subtraction CCSS: A.CED.2, A.REI.6, MP.7-y-y X single admission 50Xty y yearly membership 35.254 6.25 2660.50 *55.050 zt 12 X 50J-12*38