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12/1/2011

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.pdfNote: 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.

LaunchLaunchLaunchLaunchRead your placemat from

yesterday.

Share your steps with a partner.

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LaunchLaunchLaunchLaunchMr. 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?

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LaunchLaunchLaunchLaunchWe need equations for each so we need to

define the variables.x = time (in seconds) y = distance they

ranMeloy: y = 80 – 6.4xMershon y = 90 – 7.3x

Solve by substitution.Why don’t you see a solution on the calculator?

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

ZoomZoom

LaunchLaunchLaunchLaunchWe need equations for each so we need to

define the variables.x = time (in seconds) y = distance

they ranMeloy: y = 80 – 6.4xMershon y = 90 – 7.3x

What would be goodWindow settings?

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WINDOWXmin=Xmax =Xscl = Ymin=Ymax =Yscl = Xres=

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Team PracticeTeam Practice

I y = x + 21 4x + y = 54

II y = 4x – 5 6x + y = 55

III y = 11 – 4x 2x + y = 11

IV y = -4x + 48 8x – y = 108

How can we use the table feature of the

calculator to solve the problems?

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Team PracticeTeam Practice

I x + 2y = 28 y = 2x + 22 

II y = 2 – 3x 7x + 4y = 34     

III 10x – 5y = 172 y = -2x + 10 

IV y = -2x 40.5 7x – 14y = 72

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Team PracticeTeam Practice

I x + 2y = 28 y = 2x + 22 

II y = 2 – 3x 7x + 4y = 34     

III 10x – 5y = 172

y = -2x + 10 

IV y = -2x 40.5 7x – 14y = 72

Individual Practice

1. y = 1.5x + 2 y = -4x + 24   2. 4y + x = 45 x + 3y = 36  3. 6x + 5y = 30  x + 7y = 33Challenge. How can you use what

you’ve just learned to solve a) 4x + 1 = 9b) 2x + 4 = 5x – 2

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DebriefDebriefDebriefDebrief

What are the advantages to solve by graphing with technology?

What are the disadvantages to solve by graphing with technology?

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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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PracticePractice

Practice 6.6BYou need to use • a graphing calculator or • internet access http://my.hrw.com/math06_07/

nsmedia/tools/Graph_Calculator/graphCalc.html

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Ticket Out

Solve this system using your graphing calculator:

y = -1.5x + 25y = -4x + 45