1. ©Evergreen Public Schools 2011 1 Learning Target I can write and solve problems with two variables algebraically by using the elimination method. What does “eliminate” mean? What do you think you will eliminate? What does “eliminate” mean? What do you think you will eliminate?

2. ©Evergreen Public Schools 2011 2 LaunchLaunch Remember algebra tiles? (2 x + 1) + (4 x – 1) 6x6x

3. ©Evergreen Public Schools 2011 3 ExploreExplore

4. 4 Heidi took her daughter Lauren shopping. On Wednesday Lauren spent $95 to buy –Two pairs of jeans (sold at the same price) –One hat How much might have a pair of jeans and the hat cost? Let’s make a table of answers. Shopping

5. ©Evergreen Public Schools 2011 5 Heidi took her daughter Lauren shopping. On Wednesday Lauren spent $95 to buy –Two pairs of jeans (sold at the same price) –One hat Write an equation to represent Lauren’s shopping. Let j = price of jeans & h = price of hat + = $95 Shopping

6. ©Evergreen Public Schools 2011 6 + = $95 One way of writing equations The number and cost of what Lauren bought What she spent = Shopping j + j + c = 95 2 j + c = 95

7. ©Evergreen Public Schools 2011 7 Shopping Heidi took her daughter Lauren shopping. On Wednesday Lauren spent $95 to buy –Two pairs of jeans –One hat On Saturday Lauren spent $145 –She bought four pairs of jeans –She returned the hat How much did the jeans cost? How much did the hat cost? Read the problem.

8. ©Evergreen Public Schools 2011 8 What are methods you can use to solve this problem? Shopping

9. ©Evergreen Public Schools 2011 9 Shopping Heidi took her daughter Lauren shopping. On Wednesday Lauren spent $95 to buy –Two pairs of jeans –One hat On Saturday Lauren spent $145 –She bought four pairs of jeans –She returned the hat How much did the jeans cost? How much did the hat cost? Write a system of equations that can be used to solve the problem. Let j = price of jeans & h = price of hat

10. ©Evergreen Public Schools 2011 10 The equations Wednesday: 2j + h = $95 Saturday: 4j – h = $145 Shopping

11. ©Evergreen Public Schools 2011 11 Looking at it Differently The equations + = $95 2j + h = $95 – = $145 4j – h = $145

12. ©Evergreen Public Schools 2011 12 Looking at it Differently The equations + = $95 – = $145 How can you combine the equations? Think of how we used algebra tiles.

13. ©Evergreen Public Schools 2011 13 = $240 + = $95 – = $145 + How much does one pair of jeans cost?

14. ©Evergreen Public Schools 2011 14 Trying it with the equations 2j + h = $95 4j – h = $145 + Combine these equations in your handouts How much does one pair of jeans cost? Share your answers

15. ©Evergreen Public Schools 2011 15 Trying it with the equations The jeans cost $40 2j + h = $95 4j – h = $145 + 6j = 240 j = 40 Is this what you got?

16. ©Evergreen Public Schools 2011 16 Shopping Heidi took her daughter Lauren shopping. On Wednesday Lauren spent $95 to buy –Two pairs of jeans –One hat On Saturday Lauren spent $145 –She bought four pairs of jeans –She returned the hat How much did the jeans cost? How much did the hat cost? Read the problem again. What are you asked to find?

17. ©Evergreen Public Schools 2011 17 Trying it with the equations How do we find out how much the hat cost? 2j + h = $95 4j – h = $145

18. ©Evergreen Public Schools 2011 18 Trying it with the equations Finding out how much the hat cost. 2j + h = $95 2(40) + h = 95 80 + h = 95 h = 15 j = 40

19. ©Evergreen Public Schools 2011 19 Trying it with the equations Checking the answer in both equations Add this to your notes pages. Why does this prove the answers are correct? 2j + h = $95 2(40) + 15 = 95 80 + 15 = 95 95 = 95 h = 15 j = 40 4j – h = $145 4(40) – 15 = 145 160 – 15 = 145 145 = 145

20. ©Evergreen Public Schools 2011 20 Lauren spent $95 to buy –Two pairs of jeans –One hat Lauren spent $145 –She bought four pairs of jeans –She returned the hat Remember the original problem? In your notes pages summarize how to solve systems by elimination Jeans cost $40 Hat cost $15

21. ©Evergreen Public Schools 2011 21 Practice Solve the system of equations. 1) 2)

22. ©Evergreen Public Schools 2011 22 DebriefDebrief In your notes pages: Summarize how to solve systems of equations

23. ©Evergreen Public Schools 2011 23 5 3 1 2 4 Learning Target Did you hit the target? I can write and solve problems with two variables algebraically by using the elimination method. Rate your understanding of the target from 1 to 5. 5 is a bullseye!

24. ©Evergreen Public Schools 2011 24 Elimination Method Day 1 Practice Practice