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:
A / A

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

3. 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

4. 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.

5. 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

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 y = 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 y = 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. 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 $ After lunch, Marcus walked 14 miles and Anisa walked 13. In the afternoon they raised $ 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”