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SECTION 3: SOLVING SYSTEMS OF EQUATIONS
WITH COMBINATIONS/ELIMINATION
Homework: Pg 142 #49-55, 76, 85
Learning Target: I will solve systems of equations in real-world and mathematical situations using elimination.
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Review
When is it easiest to solve a system of equations using the graphing method?
When is it easiest to solve a system of equations using the substitution method?
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Solve the System by Graphing
y = 5x – 4y = 2x - 1
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Solve the System using Substitution
x = 2y + 3-4x + 5y = 6
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Elimination/Combination
Elimination/Combination is best used when both equations in the system are in standard form (Ax + By = C)
This method combines both equations by adding them together, but one of the variables must be eliminated as soon as the equations are combined.
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Ex 1: Solve using Elimination/Combinations
4x – 2y = 7 * Are the equations in standard form?
x + 2y = 3
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EX 2: Solve the System
2x – 3y = 6-2x + 3y = -6
• If 3x – 4y =12, can you write another equation to make the system no solutions?
•If 3x – 4y =12, can you write another equation to make the system no solutions?
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Ex 3: Elimination/Combination
Solve the system.2x – 3y = 104x + 6y = 8
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Ex 4 – Solve with Elimination
Joey and Erik go to a carnival. Joey rides the Ferris wheel 6 times and the Tilt-a-Whirl twice. Erik rides the Ferris wheel 9 times but gets sick on the Tilt-a-Whirl so he only rides it once. Joey’s fun cost $2.50 and Erik’s fun cost $2.75. How much is a ride on the Tilt-a-Whirl?
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Ex 5: Forcing an Elimination
A. 4x + 9y = 2 B. -5x + 8y = 16 2x – 5y = 6 12x + 24y = 15
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Ex 6: May the Force be with you!
3x + 7y = 15 5x + 2y = -4
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HOMEWORK
Pg 142 #49-55, 76, 85Answers:49. a) x + y = 13 4x + 2y = 38 b) 6 doubles, 7 singles50.(3, 3)51. (0, 4)52. (-5, -4)53. Many Solutions54. (-5, -3)55. (8, -6)76.Gloria is correct: see explanation85.a) 10x + 15y ≥ 350 b) see graph c) no