# 7.4 – Applications of Linear Systems - PowerPoint PPT Presentation

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7.4 – Applications of Linear Systems. Algebra 1(B). 2x + 5y = -5 x – y = 8. (5, -3). Warm-Up. Solve the following system by substitution. Objectives. Choose the best method to solve a system of linear equations. Use a system to model real-life problems. Which method should I use?.

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7.4 – Applications of Linear Systems

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## 7.4 – Applications of Linear Systems

Algebra 1(B)

2x + 5y = -5

x – y = 8

(5, -3)

Warm-Up

Solve the following system by substitution.

Objectives

Choose the best method to solve a system of linear equations.

Use a system to model real-life problems.

Which method should I use?

Graphing

Useful for approximating solutions

Provides a visual model

Substitution

Useful when one of the variables has a coefficient of 1 or -1

Linear Combination

Useful when none of the variables has a coefficient of 1 or -1

Useful when equations are written in standard form

Steps

Identify each variable.

Think: “What does each variable represent?”

Set up two equations.

Think: “How can I solve the system in the easiest way possible?”

Solve the system.

Example 1

You and your friends decide to go watch the best baseball team in town, the Chicago Cubs. There is a discount on the food at the concession stand: hotdogs are just \$1 each and cheeseburgers cost \$3 each. On one trip to the concession stand you bought 11 items that you paid \$21 for. How many hotdogs and cheeseburgers did you buy?

6 hotdogs,

5 cheeseburgers

Example 2

You and your family decide to spend the day at Six Flags Great America. The amusement park charges \$20 for each child and \$30 for each adult. A total of 10 people went and your family was charged \$230. How many children and adults attended Six Flags on that day?

7 children,

Example 3

You are comparing the prices of two pizza companies: Little Caesars and Pizza Hut. For a large pizza, Little Cesars charges \$10, plus \$0.25 for each topping. Pizza Hut charges just \$7 for a large pizza, plus \$1 for each additional topping. For how many toppings would the two companies charge the same amount of money for a large pizza?

4 toppings,

\$11 for each pizza

Partner Activity

Work on four word problems in your pairs

When you think you have the correct answer to a problem, raise your hand

A correct answer will give you a chance to win a small prize at the end of the class period