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Warm-Up Tyler is catering a banquet for 250 people. Each person will be served either a chicken dish that costs $5 each or a beef dish that costs $7 each. Tyler spent $1500. How many dishes of each type did Tyler serve? 1.) What is the question asking you to find? 2.) What are variables you could use to represent what you are trying to find? 3.) What are some important pieces of information that you would need to solve this problem? 4.) How do these numbers and variables relate?

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**Section 6.4: Applications of Linear Systems**

SWBAT choose the best method to solve a system of linear equations SWBAT use a system to model real-life problems

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**Ways to solve a system of linear equations**

Graphing Use to approximate solutions, check solutions, and provide visual models. Substitution Use when one of the variables has a coefficient of 1 or -1 Elimination Use when none of the variables have a coefficient of 1 or -1

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Example Choose a method to solve the linear system. Explain your choice. 6x + y = 2 9x – y = 28

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Example Choose a method to solve the linear system. Explain your choice. 3x + 6y = 21 -6x + 3y = -27

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**A fashion designer makes and sells hats**

A fashion designer makes and sells hats. The material for each hat costs $5.50. The hats sell for $12.50 each. The designer spends $1400 on advertising. How many hats must the designer sell to break even?

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A sporting goods store sells right-handed and left-handed baseball gloves. In one month, 12 gloves were sold for a total revenue of $ Right handed gloves cost $45 and left handed gloves cost $52. Let x represent the number of right handed gloves sold and let y represent the number of left handed gloves sold. Write a system of equations and solve to find the number of each type of glove sold.

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Goal: Solve a system of linear equations in two variables by the linear combination method.

Goal: Solve a system of linear equations in two variables by the linear combination method.

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