1. Chapter 7 – Systems of Linear Equations and Inequalities
7.4 – Applications of Linear Systems

2. 7.4 – Applications of Linear Systems
Today we will be:
Choosing the best method to solve a system of linear equations
Using a system to model real-life problems

3. 7.4 – Applications of Linear Systems
Different Methods to Solve Linear Systems
Graphing
A useful method for approximating a solution, checking the reasonableness of a solution, and providing a visual model.
Substitution
A useful method when one of the variables has a coefficient of 1 or -1.
Linear Combinations
A useful method when none of the variables has a coefficient of 1 or -1.

4. 7.4 – Applications of Linear Systems
Example 1
Your family goes to a Southern-style restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14 and some order the steak dinner for $17. If the total bill was $99 how many people ordered each dinner?

5. 7.4 – Applications of Linear Systems
Example 2
Forty of us are going the see the Philadelphia Phillies for a field trip. Each of you will receive either a hot dog or bag of popcorn. Hot dogs are $2.25 and popcorn is $ If we have $83.50 to spend, how many hotdogs can we buy?

6. 7.4 – Applications of Linear Systems
Example 3
Your family decides to visit your grandparents in Ohio. When you are in Pennsylvania, you drive at an average rate of 55 miles per hour. When you are in Ohio, you drive at an average rate of 65 miles per hour. The entire trip of 295 miles takes 5 hours. How long does it take to reach the Pennsylvania-Ohio border? How long does it take to get from the border to your grandparent’s house?

7. 7.4 – Applications of Linear Systems
HOMEWORK
Page 421
#10 – 12 (pick one), 40 – 48 even, 49, 50

8. 7.4 – Applications of Linear Systems
Example 4
An online music club offers individual songs for one price or entire albums for another. Kendrick pays $14.90 to download 5 individual songs and 1 album. Geoffrey pays $21.75 to download 3 individual songs and 2 albums. How much does it cost to download an individual song? How much does it cost to download an album?

9. 7.4 – Applications of Linear Systems
Example 5
We are traveling in two vans to the Philadelphia Zoo. Van 1 has 2 adults and 5 students. They are charged $77 for admission. Van 2 has 2 adults and 7 students. They are charged $95 for admission. How much is adult admission? How much is student admission?

10. 7.4 – Applications of Linear Systems
HOMEWORK
7.4 Practice Worksheet