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©Evergreen Public Schools 2011 1 2/1/2011 Using a Graphing Calculator to Solve Systems of Equations Teacher Notes Supplies Needed: Graphing Calculator for each student Internet Access Handouts: TI Systems.pdf TI ZOOM Settings.pdf TI Equation Solving.pdf Note: There is a section on technology on page iv of the k-12 Standards document. There are two references to Technology in the Integrated 1 Standards. They apply to linear modeling 1.6.D stating that technology is one way a student could find a best fit line & 1.7.B referring to estimating exponential solutions with and without technology. Students are not expected to be able to solve systems using technology, but using technology can help students apply problem solving skills.

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LaunchLaunch Read your placemat from yesterday. Share your steps with a partner. ©Evergreen Public Schools 2011 2

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LaunchLaunch Mr. Meloy has the football on the 20 yard line (80 yards to the end zone). Mr. Mershon (from the other team) is on the 10 yard line (90 yds to the end zone). Mr. Meloy averages 6.4 yards per second. Mr. Mershon averages 7.3 yards per sec. Will Mr. Meloy make it to the end zone before Mr. Mershon can tackle him? ©Evergreen Public Schools 2011 3

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LaunchLaunch We need equations for each so we need to define the variables. x = time (in seconds) y = distance they ran Meloy: y = 80 – 6.4 x Mershon y = 90 – 7.3 x Solve by substitution. Why don’t you see a solution on the calculator? ©Evergreen Public Schools 2011 4

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5 Follow along with the next set of slides with the Zoom Settings handout. Zoom

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LaunchLaunch We need equations for each so we need to define the variables. x = time (in seconds) y = distance they ran Meloy: y = 80 – 6.4 x Mershon y = 90 – 7.3 x What would be good Window settings? ©Evergreen Public Schools 2011 6 WINDOW Xmin= Xmax = Xscl = Ymin= Ymax = Yscl = Xres=

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©Evergreen Public Schools 2010 7 Team Practice I y = x + 21 4 x + y = 54 II y = 4 x – 5 6 x + y = 55 III y = 11 – 4 x 2 x + y = 11 IV y = -4 x + 48 8 x – y = 108 How can we use the table feature of the calculator to solve the problems?

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©Evergreen Public Schools 2010 8 Team Practice I x + 2 y = 28 y = 2 x + 22 II y = 2 – 3 x 7 x + 4 y = 34 III 10 x – 5 y = 172 y = -2 x + 10 IV y = -2 x 40.5 7 x – 14 y = 72

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©Evergreen Public Schools 2010 9 Team Practice I x + 2 y = 28 y = 2 x + 22 II y = 2 – 3 x 7 x + 4 y = 34 III 10 x – 5 y = 172 y = -2 x + 10 IV y = -2 x 40.5 7 x – 14 y = 72

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Individual Practice 1. y = 1.5 x + 2 y = -4 x + 24 2. 4 y + x = 45 x + 3 y = 36 3. 6 x + 5 y = 30 x + 7 y = 33 Challenge. How can you use what you’ve just learned to solve a)4 x + 1 = 9 b)2 x + 4 = 5 x – 2 ©Evergreen Public Schools 2010 10

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©Evergreen Public Schools 2011 11 DebriefDebrief What are the advantages to solve by graphing with technology? What are the disadvantages to solve by graphing with technology?

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©Evergreen Public Schools 2011 12 5 3 1 2 4 Learning Target Systems Target 3a I can write and solve problems with two variables using an appropriate solution with tables or graphs, and substitution or elimination.

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©Evergreen Public Schools 2010 13 Practice Practice 6.6B You need to use a graphing calculator or internet access http://my.hrw.com/math06_07/nsmedia/too ls/Graph_Calculator/graphCalc.html

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©Evergreen Public Schools 2011 14 Ticket Out Solve this system using your graphing calculator: y = -1.5 x + 25 y = -4 x + 45

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