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Solving Systems of Equations: Graphing, Substitution, and Elimination Methods

This homework assignment focuses on solving systems of equations using various methods such as graphing, substitution, and elimination. Students will practice real-world applications by tackling problems where they need to find the values of variables based on given equations. The assignment includes exercises from the textbook, providing ample opportunity to understand when to apply each method effectively. Key learning goals include mastering the elimination method for standard form equations and exploring the concept of no solutions within systems of equations.

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Solving Systems of Equations: Graphing, Substitution, and Elimination Methods

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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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