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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.

Determine your method of solution.

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

Solve the system.

Check your answer!

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,

3 adults

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

If your answer is wrong, you will need to correct it

Prizes will be given out in the last five minutes of class

EACH PERSON IN THE PAIR MUST SHOW THEIR OWN WORK ON THEIR OWN SHEET OF PAPER!

Homework

Due tomorrow:

7.4 pgs. 422-423 #31-33 (any method), 49, 50, 55