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

When to use each method Graphing Substitution Linear Combinations 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

Which method is best? Substitution Linear Combinations Substitution 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

Word Problems There will be two different situations to compare. 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.

25 minutes inline skating 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

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

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

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

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

FUNDRAISING For 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

Practice Page 367 #5

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