CHAPTER SEVEN System of Equations

PROFIT MAXIMIZATION

Chapter 7-1 System of Equations

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

System of Equation in Free Diving

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???

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

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 $ 557.5 20 $ 615.0 30 $ 672.5 40 $ 730.0 50 $ 787.5 60 $ 845.0 Revenue Formula Y=15x Total Cost Formula Y=5.75x + 500

Set Calculator Range Revenue Total Cost Break-Even Point

Break-Even Chart

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, 810.81) 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.

Practice ANSWERS

Infinitely Many Solutions Practice Infinitely Many Solutions

Check for Understanding

7-2 SUBSTITUTION

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.

7-3 Solving Using Elimination

7-4 ELIMINATION BY MULTIPLICATION

Practice

7-5 GRAPHING OF SYSTEMS OF INEQUALITIES

7-5 GRAPHING OF SYSTEMS OF INEQUALITIES

Practice

CLASSWORK Pg 397