Corny Joke Applications of Linear Systems Goals Choose

Corny Joke

Applications of Linear Systems Goals: • Choose the best method to solve a system of linear equations • Use a system to model real-life problems

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

Which method is best? � 2 x + 3 y = 4 �-3 x + y = 9 �y = 2 x + 1 � 5 x – 2 y = 9 Linear Substitutio Linear 4 x – 2 y = 8 5 x + 2 y = 10 n Combination s � 4 x + y = 3 Substitutio �y = 7 x + 1 Graphin 5 x + 5 y = 16 n y =½ x – 3 g Graphin y = 3 x – 5 g 3 x + 2 y = 7 Combination s

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

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 Calories: 8 x + 12 y = 380 Minutes: x + y = 40 x = inline skating y = swimming 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: 2 x + 2. 50 y = 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? Company A Slope-Intercept Form Company B m=2 m =. 50 b = 12 b = 27 y = 2 x + 12 y =. 50 x + 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 Money: 3 x + 1. 50 y = 12 Points: 5 x + 3 y = 22 x = new releases y = regular movies 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? Company A Slope-Intercept Form Company B m = 25 m = 35 b = 150 b=0 y = 25 x + 150 y = 35 x + 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

Homework: EDGENUITY

Homework: EDGENUITY

Homework: EDGENUITY