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Solving Systems of Equations: Graphing, Substitution & Linear Combination Techniques

This lesson focuses on finding solutions to systems of equations using three methods: graphing, substitution, and linear combination. The provided equations include (2x + y = 60) and (x + 2y = 75). The objectives are to apply these techniques in real-life situations, such as determining the cost of movie tickets and popcorn. Additional problems include distance calculations and investment scenarios, encouraging a comprehensive understanding of algebraic principles. Homework is assigned for further practice.

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Solving Systems of Equations: Graphing, Substitution & Linear Combination Techniques

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  1. 4.3 Algebra 2 Brett Solberg AHS 2011-2012

  2. Warm-up • Find the solution of the equations by graphing, substitution, and linear combination. • 2x + y = 60 • x + 2y = 75 (make your graph in intervals of 10)

  3. Test Recap • 2nd Average 30/40 = 75% • High 42 • 4th Average 28/40 = 70% • High 43 • Make-up Options • Correct on separate paper • Staple to test • Turned in this week • Missing Review • PTC Extra Credit

  4. Today’s Objectives • Finding solutions of systems of equations in real-life situations. • Graphing • Substitution • Linear Combination

  5. Night at the movies. • George bought two movie tickets and a large popcorn for $20. The next day he went and bought 3 movie tickets and 2 large popcorns for $32.50. How much was an individual movie ticket and popcorn? • Problem Solving Guidelines • 1) Understand the problem • What is the problem asking? • What do we know? • 2) Develop and carry out a plan. • Write out equations. • 3) Find the answer and check. • Solve

  6. Weedkiller x + y = 100 .05x + .15y = 12

  7. Milk

  8. Distance = Rate * Time • You are traveling 60 mph. • How far have you driven in one hour? Two hours? 10 hours? • D = 60 * 1 = 60 miles • D = 60 * 2 = 120 miles • D = 60 * 10 = 600 miles

  9. Train Problems 35 km/h t + 2 Phoenix Train Station 40 km/h t d = 35(t + 1) d = 40t

  10. Investments x + y = $15,000 .09x + .10 y = $1432

  11. Homework • 4.3 pg. 171 #3-30, multiples of 3

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