Transcript Elimination Method

Do Now
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1.
2.
3.
Rewrite each equation for x.
Then rewrite each equation for y.
Y+1=x
2x + 3y = 6
Y + 2x = 3
Elimination Method
Coordinate Algebra
Standard: A.REI.6
Essential Question
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How do I solve a system of equations using
the ELIMINATION method?
Motivation for the Lesson
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I am thinking of two numbers whose sum is
30 and whose difference is 10. What are the
two numbers?
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Answers: 20 and 10
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Can this riddle be solved using a system of
equations?
Elimination Method
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Algebraic Method for solving a system of
equations using the sum of like terms to
eliminate one of your variables.
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Looking for opposite coefficients in front of
either x or y so they will add to = zero.
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You must FIND or CREATE opposites!!!
Ex 1)
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Solve by elimination.
3x  4y  12
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3x  6y  18
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Answer: (-24, -15)
Ex 2)
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Solve the system using elimination.
6x  5y  4
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6x  7 y  20
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Answer: ( -1, 2)
Ex 3)
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Solve by Elimination.
2x  3y  7
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3y  7  2x
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Answer: no solution
Ex 4)
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Solve by Elimination
4x  y  12
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1
x  3  4 y
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Answer: infinitely many solutions
Ex 5) Word Problems
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Find two numbers whose sum is 64 and whose
difference is 42.
x  y  64
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x
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y
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42
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Answer: 11 and 53
Bonus: Use Elimination twice.
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Write answer as an ordered triple (x, y, z).
x  y  2z  8
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2x  y  z  13
4x  3z  7
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Answer: (4, 2, 3)
Summarizer
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Can you give an example of a system of
equations in which both variables would be
eliminated? What is the solution of your
system of equations?
Graphic Organizer
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Let’s walk through it…
Homework
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worksheet