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Systems of Linear Equations Chapter QuestionsWhat are the different ways to solve a system of linear equations?When do you get an answer to a system of linear equations that has one solution, no solution and infinitely many solutions?Systems of Linear Equations Chapter ProblemsSolving Systems by GraphingClassworky = -x – 7y = 43x – 7y = - 14x + 2y = - 12x + 3y = -3x – 5y = x + 3 y = -2x + 5y = 13x – 2y = -4x + 7y = -3x + 3y = 34x – 3y = 34x + 23x + 2y = 2x + 2y = -2x + 3y = -92x – y = -4x – 2y = 2x + 4y = -85x + y = -2x + y = 2Homeworky = - 32x – 4y = - 12 + 1y = -2x – 2y = -3x – 6y = x – 2y = x + 2y = 34x + 1y = - 12x – 4y = x – 4y = -x + 2x + y = 24x – y = -44x – y = -3x + y = -2x + 2y = 8x – y = 2x – 3y = -32x + 3y = 122x – 3y = 3x + 3y = -12Solving Systems by SubstitutionClassworkx = 4y – 9x = y + 35x = -2y + 48x = -3y + 20y – 4x = 28y = -2x – 2y + 2x = -12y = x + 15x = -2y – 72x + y = -14x = 5y – 38x = -4y + 16y = 2x + 34x – 2y = 84x + y = -6-6x + 2y = 166x – 2y = 8-3x + y = -4-2x + 7y = 15-3x – 8y = 4Homeworky = -5x + 41-2x = -14 – 2yy = 3x + 6-6x + 2y = 12y – 3x = 0y = -3x – 18x = -3y + 134x – 4y = 20x = -4y + 295x + 2y = 37y = -2x + 115y – 2x = 315y – 5x = -15y = -3x + 29-2x + 4y = 1x – 2y = -1-6x + y = -125x + 4y = 10-2x – 3y = 9-x – y = 2 Solving Systems by EliminationClasswork3x + y = 365x + y = 56x + 2y = 25x + 3y = 333x – 5y = -52x – 5y = -342x + 3y = 4-2x + 5y = 602x + 2y = 25x – 2y = 405x – 4y = 47-x – 16y = 1253x – 2y = 33-4x – 4y = 162x + y = 214x + 3y = 51-3x + 3y = -2712x + 5y = 1083x + 4y = 3-12x – y = -572x + 5y = -78x + 3y = 574x + 3y = 338x + y = 31-7x – 5y = 21-10x – 8y = 2416x + 16y = -16-12x – 12y = 12-6x – 10y = 2210x – 3y = -17Homework4x – y = -24x + 5y = 102x + 4y = 10-4x + 4y = 52-3x – 5y = 493x + 4y = -44-4x + 3y = 395x – 3y = -45-5x – 2y = -5-x – 2y = -1–x + y = -5-3x + 4y = -12-2x – y = 2-6x + 3y = -18-2x + 2y = 166x – y = -13-4x – 5y = -93x + 10y = 133x – 2y = -266x – 4y = -70x + 5y = -123x + y = 6x + y = 144x – 2y = 2-50x + 50y = 020x – 20y = -207x – 4y = -18-4x + 3y = 113x + 4y = -42x – 7y = 7Choosing Your StrategyClasswork–x + 4y = 5x + 4y = 113x – y = 74x – 2y = 82y + 5x = 35y = 4x – 285x – 4y = -39-3x – 4y = -15y = -5x + 594x + y = 49y = x + 6y = 45x + 6 -2x + 4y = 282x – 3y = -18y = -x + 123y + 3x = 362x + 4y = -10-4x – 12y = 36–x – 5y = -3-2x + 5y = 9Choosing Your StrategyHomework-3x + 5y = -3912x – 4y = 60y = 3x – 18y – 3x = -24x + 3y = 16-x + 4y = 5x = -3y – 19x + 5y = -223x – 3y = 129x + 2y = 102y = - 43x + 4y = 23x + 103x + 2y = 21-3x + 5y = 21–x – y = 7-x + 5y = 194x + y = -28-2x + 2y = 24x = 2y – 7-x + 4y = 17Writing Systems to Model SituationsClassworkPARCC-type Questions:The admission fee at a carnival is $3.00 for children and $5.00 for adults. On the first day 1,500 people enter the fair and $5740 is collected. How many children and how many adults attended the carnival?A builder placed two orders with the hardware store. The first order was for 25 sheets of plywood and 4 boxes of nails and the bill totaled $357. The second order was for 35 sheets of plywood and 2 boxes of nails and the bill totaled $471. The bills do not list the per-item price. What were the prices of one piece of plywood and one box of nails?You bought 12 bottles of orange juice and apple juice. The apple juice was on ale for $1.00 per bottle, and the orange juice was on sale for $1.75 per bottle. How many bottles of each type of juice did you buy if you spent $15.00?Last year, you mowed grass and shoveled snow for 10 households. You earned $200 per household mowing lawns, and $180 per household shoveling snow. If you earned a total of $1,880 in one year, how many households did you mow and shovel for?Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of friends purchased 6 tickets for $40. How many of each type of ticket were sold?HomeworkPARCC-type Questions:Two friends bought some markers and pens. The first bought 4 markers and 5 pens and it cost him $6.71. The second friend bought 5 markers and 3 pens, which cost her $7.12. What is the price for one marker and one pen?The ticket price for the movies is $7.50 for children and $10.50 for adults. One night 825 people bought tickets and $8005.50 was collected from ticket sales. How many children and how many adults bought tickets.You bought 16 bottles of grape juice and lemonade. The grape juice was on ale for $1.25 per bottle, and the lemonade was on sale for $1.50 per bottle. How many bottles of each type of juice did you buy if you spent $21.50?Last year, you mowed grass and shoveled snow for 15 households. You earned $180 per household mowing lawns, and $160 per household shoveling snow. If you earned a total of $2,560 in one year, how many households did you mow and shovel for?Tickets to a movie cost $7.50 for adults and $5.75 for students. A group of friends purchased 10 tickets for $61.00. How many of each type of ticket were sold?Unit ReviewUse the equations below to answer the questions:y = x + 8x + 3y = 12Part A:Graph the system of equations in the coordinate plane below.Part B: Which point is the point of intersection? (-5, 3)(7, 1)(6, 2)(-3, 5)Solve the system:-x + 4y = 125x - 2y = -6Solve the system:y = 3x – 72x - 5y = 22What is the value of y in the following system of equations?x + 5y = 7x – 3y = –112-34Use the equations below to answer the questions:3x + 4y = 129x + 12y = 36Part A:Graph the system of equations in the coordinate plane below.Part B:Which point is the point of intersection?No solutionIntersect at (0, 5)Intersect at (0, 0)Infinitely many solutionsSolve the system:3x + 2y = 82x + 3y = 7Solve the system:y = 6x - 1y = x + 4If the graph of a system shows two parallel lines, thenthere are infinite solutionsthere is no solutionthere may be a solution if the lines are extendedsomething is incorrect with the graphUse the equations below to answer the questions:3x + y = 6-3x + y = -6Part AGraph the system of equations in the coordinate plane below.Part BWhich point is the point of intersection? (2, 1)(0, 2)(2, 0)(3, 3)Solve the system: x = 2y – 6x = -3y – 14?What is true of the graphs of the two lines 3x + 5y = -9 and -6x - 10y = -12?No solutionIntersect at (-3,0)Intersect at (2,-5)Infinitely many solutionsTo solve 4x + 2y = 10 and x + y = 4 by elimination,first multiply the second equation by -2 first multiply the second equation by -1 first multiply the second equation by 2first multiply the second equation by 4Bob wants to sub 3x + y = 13 into 4x + 3y = 6, he needs toconvert the equation to 3x = 13 – y convert the equation x = 13 – yconvert the equation to y = 13 – 3x convert the equation to x = -y – 13 What is the value of the y-coordinate of the solution to the system of equations -3x + y = 9 and x ? y = 7?623-15Sketch a graph of a system that has infinitely many solutions.Sketch a graph of a system that has no solution.-+gb5141023120=÷?Five time as many girls as boys went to the dance. The total of 120 students went to the dance.Part AIf b represents the number of boys and g represents the number of girls, use the numbers, variables, and symbols shown below to construct a system of equations to model this situation. Some of the numbers, variables, and operations will be used more than once and some will not be used at all.Part BDetermine the number of boys and girls went to the dance.5$4.00$140.00$2.504$5.00=÷?-+yx$2.00The elementary school students are putting on a play as a fundraiser. The student tickets cots $2.00 each and the adult tickets cost $4.00 each. They sold 5 times as many student tickets as adult tickets. They made $140.00. Part AIf x represents the number of student tickets sold and y represents the number of adult tickets sold, use the numbers, variables, and symbols shown below to construct a system of equations to model this situation. Some of the numbers, variables, and operations will be used more than once and some will not be used at all.Part BDetermine the number of student and adult tickets were sold.Do you love numbers enough to have one as your name? Looks like a lot of Americans do, or at least their parents liked the idea when naming their baby. Turns out more than 1,500 people?are named Seven! And you're probably wondering, is that a girl's name or a boy's name? Both men and women have the name, but just 484 women compared to 1,100 men. No other number between 1 and 20, like Two, Six or Eleven, showed up as a name for more than a few people - Seven was the big winner. Of course, some names have numbers in them, too. The number "ten" leads the way, with 211,000 people named Kristen. "One" shows up in Tyrone, Simone and other names. Even "eight" can be found hidden in Leighton and Peighton. See if you can spot any numbers in your own name- and if not, you can always change your name to a lucky Seven.If you and 5 friends get together, and you're all named Seven or Six, and your names add up to 38...how many of each name do you have?Problem found at ’s super exciting when we find the bones and teeth of animals from long ago. In the case of the megalodon, we might be just as happy this giant ocean creature isn’t around any more! As Bedtime Math fans Mary Claire A. and son Gavin just shared, this past week a regular guy wandering down a beach found what turned out to be a fossilized megalodon tooth (“fossilized” means it has turned into rock over time). You can tell from the huge tooth that this shark-like animal must have been huge, too: scientists think megalodons were 60 feet long. The animals lived from 15 million to 5 million years ago…for comparison, dinosaurs died out completely by 65 million years ago. Some people want to believe that there are still giant shark-like megalodons swirling around deep in the ocean. No one has seen any proof of that yet, but maybe someone will be brave enough to go looking for one.If a megalodon had 5 times as many teeth as you’ve lost so far, and that’s also 60 more than you’ve lost, how many teeth did the megalodon have?Problem found at Telephone company A charges $20 per month and $0.10 per text. Telephone company B charges $15 per month and $0.20 per text. Let t = the number of texts and C = cost.Write an equation to represent the cost of each plan.Solve the system by graphing.Explain what the solution to the system means in terms of what telephone company to provide services.Answer Keyx=0, y=-7x=4, y=1x=-2, y=1x=3, y=-1x=4, y=-9No solutionx=2, y=-2x=-3, y=-2x=-4, y=-1x=-1, y=3x=-5, y=3.5x=-4, y=6No solutionx=-4, y=-2x=3, y=-1x=-2, y=-4x=-1, y=-1x=4, y=2x=3, y=2x=-3, y=-3x=7, y=4x=8, y=4x=-5, y=8x=-9, y=6x=-7, y=0x=-8, y=6No solutionx=-2, y=2x=-4, y=1x=-5, y=7x=8, y=1Same functionx=-3, y=-9x=7, y=2x=5, y=6x=2, y=7x=8, y=5no solutionx=2, y=0x=3, y= -5x=10, y=6x=9, y=8x=-9, y=5x=-10, y=8x=6, y=-5x=3, y=-8x=5, y=-9x=6, y=9x=9, y=0x=5, y=-3x=9, y=-5x=3, y=7x=-8, y=7infinite solutionsx=-2, y=-1x=0, y=2x=7, y=6x=8, y=-5x=-6, y=5x=1, y=0x=8, y=3x=1, y=-4x=-1, y=7x=1, y=1No solutionx=3, y=-3x=5, y=9no solutionx=-2, y=1x=0, y=-1x=3, y=2x=3, y=2x=7, y=0x=-3, y=6x=10, y=9x=0, y=6x=6, y=10x=0, y=12x=3, y=-4x=-2, y=1x=3, y=-6No solutionx=7, y=3x=-14.5, y=-1.5x=10, y=6x=-3, y=8x=3, y=6x=-9, y=2x=-8, y=4x=3, y=5Adults: 620, Children: 880Plywood: $13, Box of nails: $88 bottles of apple juice & 4 bottles of orange juicemowed lawns of 4 households and shoveled snow for 6 households4 adults & 2 studentsPen: $0.39, Marker: $1.19Children: 219, Adults 60610 bottles of grape juice & 6 bottles of lemonademowed lawns for 8 households and shoveled snow for 7 households2 adults and 8 studentsReview AnswersPart A:Part B: D(0, 3)(1, -4)APart A:Part B: D(2, 1)(1, 5)BPart A:Part B: C(-9.2, -1.6)AACDAnswers vary; Sample Answer:Answers vary; Sample Answer:Part A:g = 5bb + g = 120Part B:20 boys & 100 girlsPart A: 2x + 4y = 140x = 5yPart B:10 adults and 50 students2 people named “Seven”2 people named “Six”The megalodon had 75 teethC = .10t + 20C = .20t + 15The plans cost the same with 50 text messages. If purchasing a plan with less than 50 text messages, company B has a better price. If purchasing a plan with more than 50 text messages, company A has a better price. ................
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