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CHAPTER SEVEN System of Equations.

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Presentation on theme: "CHAPTER SEVEN System of Equations."— Presentation transcript:

1 CHAPTER SEVEN System of Equations

2 PROFIT MAXIMIZATION

3 Chapter 7-1 System of Equations

4 System of Equations- Two or more equations which contain the SAME VARIABLES
Which of the following are systems??? Yes: Same Variables Yes: Same Variables No: Different Variables

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6 System of Equation in Free Diving

7 System of Equations in Business
We are going to start a T-shirt business. Our fixed cost (rent for the building) is $500 Our Variable cost (Ink, T-shirts) is $5.75 a shirt. We are going to sell our shirts for $15.00 each. How many shirts do we need to sell in order to Break-Even???

8 Fill in the Tables and Write an equation for each function.
# of T-Shirts Revenue 10 20 30 40 50 60 # of T-Shirts Total Cost 10 20 30 40 50 60

9 Graph each equation in your calculator.
# of T-Shirts Revenue 10 $150.0 20 $300.0 30 $450.0 40 $600.0 50 $750.0 60 $900.0 # of T-Shirts Total Cost 10 $ 20 $ 30 $ 40 $ 50 $ 60 $ Revenue Formula Y=15x Total Cost Formula Y=5.75x + 500

10 Set Calculator Range Revenue Total Cost Break-Even Point

11 Break-Even Chart

12 Revenue Formula Total Cost Formula Y=15x Y=5.75x + 500 (54.05, 810.81)
What are the coordinates of the intersection point??? And what do they represent??? (54.05, ) Revenue Formula Y=15x Total Cost Formula Y=5.75x + 500 Y=15(54) Total Revenue= $810 Y=5.75(54) + 500 Total Cost= $810.50 54 shirts must be sold in order to break-even.

13 Practice ANSWERS

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16 Infinitely Many Solutions
Practice Infinitely Many Solutions

17 Check for Understanding

18 7-2 SUBSTITUTION

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23 Substitution may result in a more accurate
solution than graphing. Since the statement 4 = 2 is false, there are no solutions of the system of equations. This means that the graphs do not intersect, so they are graphs of parallel lines.

24 7-3 Solving Using Elimination

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29 7-4 ELIMINATION BY MULTIPLICATION

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33 Practice

34 7-5 GRAPHING OF SYSTEMS OF INEQUALITIES

35 7-5 GRAPHING OF SYSTEMS OF INEQUALITIES

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38 Practice

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40 CLASSWORK Pg 397

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