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6-5 Applications of Linear Systems

6-5 Applications of Linear Systems

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6-5 Applications of Linear Systems

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  1. 6-5 Applications of Linear Systems Goals: Choose the best method to solve a system of linear equations Use a system to model real-life problems Eligible Content: A1.1.2.2.1 / A1.1.2.2.2

  2. When to use each method • Graphing • If equations are in slope intercept form • If the problem involves inequalities • If numbers are small and easy to graph • Substitution • If there is a variable without a number in front of it • Linear Combinations • If all variables have numbers in front

  3. Which method is best? • 2x + 3y = 4 4x – 2y = 8 • 4x + y = 3 5x + 5y = 16 • y = 2x + 1 y = 3x – 5 • -3x + y = 9 5x + 2y = 10 • y < 7x + 1 y ≥ ½ x – 3 • 5x – 2y = 9 3x + 2y = 7 Substitution Linear Combinations Substitution Graphing Linear Combinations Graphing

  4. Word Problems Slope-Intercept Form Standard Form There will be two different situations to compare. You are given a slope and a y-intercept for each situation. Write y = mx + b equations. There will be two different things you are looking for. All of the numbers will fall into two categories. Write Ax + By = C equations.

  5. Word Problem #1 You want to burn 380 calories during 40 minutes of exercise. You burn about 8 calories per minute inline skating and 12 calories per minute swimming. How long should you spend doing each activity? Standard Form x = inline skating y = swimming Calories: 8x + 12y = 380 Minutes: x + y = 40 25 minutes inline skating 15 minutes swimming

  6. Word Problem #2 Selling frozen yogurt at a fair you make $565 and use 250 cones. A single-scoop cone costs $2 and a double-scoop cone costs $2.50. How many of each type of cone did you sell? Standard Form x = single-scoop y = double-scoop Money: 2x + 2.50y = 565 Cones: x + y = 250 120 single-scoop cones 130 double-scoop cones

  7. Word Problem #3 You have a choice of two different Internet service companies. Company A charges $12 each month plus $2 per hour. Company B charges $27 each month plus $.50 per hour. How many hours would you need to use the Internet for the two companies to be the same? Slope-Intercept Form Company A m = 2 b = 12 y = 2x + 12 Company B m = .50 b = 27 y = .50x + 27 10 hours

  8. Word Problem #4 You enroll in a movie club where you earn points to use toward future rentals. Each new release costs $3 and earns 5 points. Each regular movie costs $1.50 and earns 3 points. On your recent rental you paid $12 and earned 22 points. How many of each type of movie did you rent? Standard Form x = new releases y = regular movies Money: 3x + 1.50y = 12 Points: 5x + 3y = 22 2 new releases 4 regular movies

  9. Word Problem #5 A retailer offers two options for satellite TV service. A customer may buy the dish for $150 and then pay $25 per month for service. The other option is to rent the dish for free and pay $35 per month for service. After how many months will the two companies be the same? Slope-Intercept Form Company A m = 25 b = 150 y = 25x + 150 Company B m = 35 b = 0 y = 35x + 0 15 months

  10. FUNDRAISINGFor a school fundraiser, Marcus and Anisa participated in a walk-a-thon. In the morning, Marcus walked 11 miles and Anisa walked 13. Together they raised $523.50. After lunch, Marcus walked 14 miles and Anisa walked 13. In the afternoon they raised $586.50. How much did each raise per mile of the walk-a-thon? A. Marcus: $22.00, Anisa: $21.65 B. Marcus: $21.00, Anisa: $22.50 C. Marcus: $24.00, Anisa: $20.00 D. Marcus: $20.75, Anisa: $22.75

  11. Practice • Page 367 #5

  12. Homework • Worksheet – “6-5 Applications of Linear Systems Homework #1”