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Section 3: solving Systems of Equations with combinations/elimination

Homework: Pg 142 #49-55, 76, 85. Section 3: solving Systems of Equations with combinations/elimination. Learning Target: I will solve systems of equations in real-world and mathematical situations using elimination. Review.

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Section 3: solving Systems of Equations with combinations/elimination

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  1. Homework: Pg142 #49-55, 76, 85 Section 3: solving Systems of Equations with combinations/elimination Learning Target: I will solve systems of equations in real-world and mathematical situations using elimination.

  2. 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?

  3. Solve the System by Graphing y = 5x – 4 y = 2x - 1

  4. Solve the System using Substitution x = 2y + 3 -4x + 5y = 6

  5. 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.

  6. Ex 1: Solve using Elimination/Combinations 4x – 2y = 7 * Are the equations in standard form? x + 2y = 3

  7. 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?

  8. Ex 3: Elimination/Combination Solve the system. 2x – 3y = 10 4x + 6y = 8

  9. 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?

  10. Ex 5: Forcing an Elimination A. 4x + 9y = 2 B. -5x + 8y = 16 2x – 5y = 6 12x + 24y = 15

  11. Ex 6: May the Force be with you! • 3x + 7y = 15 5x + 2y = -4

  12. HOMEWORK • Pg 142 #49-55, 76, 85 Answers: 49. a) x + y = 13 4x + 2y = 38 b) 6 doubles, 7 singles (3, 3) (0, 4) (-5, -4) Many Solutions (-5, -3) (8, -6) Gloria is correct: see explanation a) 10x + 15y ≥ 350 b) see graph c) no

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