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

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

16. Infinitely Many Solutions
Practice
Infinitely Many Solutions

17. Check for Understanding

18. 7-2 SUBSTITUTION

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

29. 7-4 ELIMINATION BY MULTIPLICATION

33. Practice

34. 7-5 GRAPHING OF SYSTEMS OF INEQUALITIES

35. 7-5 GRAPHING OF SYSTEMS OF INEQUALITIES

38. Practice

40. CLASSWORK Pg 397