©Evergreen Public Schools 2011 1 Learning Target I can write and solve problems with two variables algebraically by using the elimination method. What.

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©Evergreen Public Schools 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?

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

©Evergreen Public Schools ExploreExplore

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

©Evergreen Public Schools 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

©Evergreen Public Schools = $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

©Evergreen Public Schools 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.

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

©Evergreen Public Schools 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

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

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

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

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

©Evergreen Public Schools 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

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

©Evergreen Public Schools 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?

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

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

©Evergreen Public Schools 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 h = 15 j = 40 4j – h = $145 4(40) – 15 = – 15 = = 145

©Evergreen Public Schools 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

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

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

©Evergreen Public Schools 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!

©Evergreen Public Schools Elimination Method Day 1 Practice Practice