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CHAPTER SEVEN System of Equations
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PROFIT MAXIMIZATION
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Chapter 7-1 System of Equations
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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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System of Equation in Free Diving
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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???
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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
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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
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Set Calculator Range Revenue Total Cost Break-Even Point
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Break-Even Chart
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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.
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Practice ANSWERS
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Infinitely Many Solutions
Practice Infinitely Many Solutions
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Check for Understanding
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7-2 SUBSTITUTION
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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.
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7-3 Solving Using Elimination
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7-4 ELIMINATION BY MULTIPLICATION
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Practice
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7-5 GRAPHING OF SYSTEMS OF INEQUALITIES
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7-5 GRAPHING OF SYSTEMS OF INEQUALITIES
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Practice
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CLASSWORK Pg 397
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