7.4 – Applications of Linear Systems Algebra 1(B).
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Transcript of 7.4 – Applications of Linear Systems Algebra 1(B).
![Page 1: 7.4 – Applications of Linear Systems Algebra 1(B).](https://reader035.fdocuments.in/reader035/viewer/2022072016/56649ef35503460f94c06826/html5/thumbnails/1.jpg)
7.4 – Applications of Linear Systems
Algebra 1(B)
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Solve the following system by substitution.
Warm-Up
2x + 5y = -5x – y = 8 (5, -3)
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1. Choose the best method to solve a system of linear equations.
2. Use a system to model real-life problems.
Objectives
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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
Which method should I use?
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1. Identify each variable.o Think: “What does each variable
represent?”2. Set up two equations.3. Determine your method of solution.
o Think: “How can I solve the system in the easiest way possible?”
4. Solve the system.5. Check your answer!
Steps
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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?
Example 1
6 HOTDOGS,5 CHEESEBURGERS
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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?
Example 2
7 CHILDREN,3 ADULTS
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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?
Example 3
4 TOPPINGS,$11 FOR EACH PIZZA
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• 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!
Partner Activity
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Due tomorrow:
7.4 pgs. 422-423 #31-33 (any method), 49, 50, 55
Homework