©evergreen public schools 2011 1 learning target i can write and solve problems with two variables...
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©Evergreen Public Schools 2011
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• I can write and solve problems with two variables algebraically by using the elimination method.
What is the elimination method?
What is the elimination method?
©Evergreen Public Schools 2011
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LaunchLaunchLaunchLaunchSimone work on her Science Fair project.
She bought 5 markers and 2 highlighters on Monday for $8.23 before tax. Wednesday she spent $5.65 on 3 more markers and 2 more highlighters.
Write and solve a system of equations to find how much Simone paid for one marker.
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Solve for x.
What would this system of equations have to look like so you could use the elimination method?
How could you get the system to look that way?
More Elimination MethodMore Elimination Method
3x y6
2x5y55
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Solve for x.We can multiply the top equation by 5
More Elimination MethodMore Elimination Method
3x y6
2x5y55 5( 3x y)(6)5
15x 5y30
2x5y55
17x 85
x 5
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What do you have to do the one or both equations to solve with the elimination method?
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4x 2y 4
2x3y10
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Make sure equations are in standard form. Decide whether the x or y coefficients would be easiest to eliminate by adding the two equations together.
Decide what to multiply each equation by so that when you add the two, the variable will be eliminated.
Work though this one in your
notes pages
More Elimination MethodMore Elimination Method
4x 2y 4
2x3y10
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4x – 2y = -4 2x + 3y = 10
4x – 2y = -4 -2 (2x + 3y = 10)
4x – 2y = -4 + -4x – 6y = -20
0x – 8y = -24
y = 3
Solve for x:
2x + 3y = 10
2x + 3(3) =
10
2x + 9 = 10
2x = 1
x = ½
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Check the solution in each equation: x = ½ y = 3
2x + 3y = 10
2 (½) + 3(3) = 10
1 + 9 = 10
10 = 10
4x – 2y = -4
4(½) – 2(3) = -4
2 – 6 = -4
-4 = -4
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Solve the system of equations1) 5x + y = 9 2) –4x + 9y = 18 10x – 7y = – 18 x + 3y = 27
• –7x + y = – 19 4) 3x – 7y = 45 – 2x + 3y = – 19 –9x + 5y = –87
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Team PracticeTeam PracticeThe manager for the professional soccer team, the Portland Timbers, wants to have a promotional game where she gives away sports bags and caps to fans.
•She can buy bags for $12 and caps for $15.
•The total budget for the promotion is $53,100
•She plans to give the first 4000 fans either a bag or a cap, but not both.
•How many bags and caps can she give away?
Work though this one in your
notes pages
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• Share variables and equations
• Share how many bags and caps can be given away
Team PracticeTeam Practice
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DebriefDebriefDebriefDebriefIn your notes pages:
• Summarize how to solve systems of equations with the elimination method.
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5
3
12
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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!
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• Finish “Elimination Method Practice Day 2”
PracticePractice