1. ©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.

2. ©Evergreen Public Schools 2011 2 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. What methods can you use to solve systems of equations?

3. LaunchLaunch Emika and Heidi decided to walk for a walkathon fundraiser. For each mile they walk. Emika has collected $1 in donations and $3 per mile in pledges. Heidi has collected $3 in donations and $2 per mile in pledges. How many miles will each girl have to walk in order for both of them to raise the same amount? ©Evergreen Public Schools 2011 3

4. LaunchLaunch x = # mile walked y = $ collected Emika: y = 3 x + 1 Heidi : y = 2 x + 3 How many miles will each girl have to walk in order for both of them to raise the same amount? ©Evergreen Public Schools 2011 4

5. 5 ExploreExplore

6. 6 y = - 2 x + 9 y = 3 x – 4 What is the solution? Today we’ll see a new way to solve by graphing Solve

7. ©Evergreen Public Schools 2011 7 Follow along on your own graphing calculator as we solve the following system using a graphing approach: Follow handout…. y = 3 x – 4 y = - 2 x + 9 Input Equations

8. ©Evergreen Public Schools 2011 8 Read the solution from your calculator. How would you record the solution? What does the solution mean? Find the Solution

9. x = # mile walked y = $ collected Emika: y = 3 x + 1 Heidi : y = 2 x + 3 How many miles will each girl have to walk in order for both of them to raise the same amount? How would you record the solution? What does the solution mean? ©Evergreen Public Schools 2011 9

10. ©Evergreen Public Schools 2010 10 Team Practice I y = 3 x – 4 y = -3 x + 2 II y = 4 x – 1 y = - x + 4 III y = 2 – x y = x – 4 IV y = 3 x + 4 y = -6 x – 4

11. ©Evergreen Public Schools 2010 11 Team Practice I screen dump II y = 4 x – 1 y = - x + 4 III y = 2 – x y = x – 4 IV y = 3 x + 4 y = -6 x – 4

12. ©Evergreen Public Schools 2010 12 Team Practice I -3 x + y = 17 y + x = 5 II y = -4 x + 18 5 y – 4 x = 42 III y = - x + 5 3 y = x – 23 IV y = -5 x – 34 -3 x = 14 – y

13. ©Evergreen Public Schools 2010 13 Team Practice I -3 x + y = 17 y + x = 5 Y1 = Y2 = II y = -4 x + 18 5 y – 4 x = 42 Y1 = Y2 = III y = - x + 5 3 y = x – 23 Y1 = Y2 = IV y = -5 x – 34 -3 x = 14 – y Y1 = Y2 =

14. ©Evergreen Public Schools 2010 14 Team Practice I screen dumpII y = -4 x + 18 5 y – 4 x = 42 Y1 = Y2 = III y = - x + 5 3 y = x – 23 Y1 = Y2 = IV y = -5 x – 34 -3 x = 14 – y Y1 = Y2 =

15. ©Evergreen Public Schools 2011 15 5 3 1 2 4 Learning Target Did you hit the 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.

16. Placemat ©Evergreen Public Schools 2010 16 Use your handouts to write the step for solving a system of equations on the graphing calculator. Name 1 Name 2 Name 3 Name 4

17. ©Evergreen Public Schools 2010 17 Practice Practice 9.6A You need to use a graphing calculator or internet access http://my.hrw.com/math06_07/nsmedia/too ls/Graph_Calculator/graphCalc.html I’ll show you how. Graphing calculator app for smartphone iPhone – Free GraCalc Android?