1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 1 Homework, Page 604 Use substitution to solve the system of equations. 1.

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 2 Homework, Page 604 Use Gaussian elimination to solve the system of equations. 5.

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 3 Homework, Page 604 Perform the indicated elementary row operations on the matrix. 9.

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 4 Homework, Page 604 What elementary row operations applied to the matrix will yield the given matrix. 13.

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 5 Homework, Page 604 Find a row echelon form for the matrix. 17.

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 6 Homework, Page 604 Find the reduced row echelon form for the matrix. 21.

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 7 Homework, Page 604 Write the augmented matrix corresponding to the system of equations. 25.

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 8 Homework, Page 604 Write the system of equations corresponding to the augmented matrix. 29.

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 9 Homework, Page 604 Solve the system of equations by finding a row echelon form for the augmented matrix. 33.

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 10 Homework, Page 604 Solve the system of equations by finding the reduced row echelon form for the augmented matrix. 37.

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 11 Homework, Page 604 Solve the system of equations by finding the reduced row echelon form for the augmented matrix. 41.

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 12 Homework, Page 604 Write the system of equations as a matrix equation AX = B, with A as the coefficient matrix of the system. 45.

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 13 Homework, Page 604 Solve the system of equations by using an inverse matrix. 49.

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 14 Homework, Page 604 Solve the system of equations by using an inverse matrix. 53.

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 15 Homework, Page 604 53.

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 16 Homework, Page 604 Use the method of your choice to solve the system of equations. 57.

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 17 Homework, Page 604 Use the method of your choice to solve the system of equations. 61.

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 18 Homework, Page 604 Use the method of your choice to solve the system of equations. 65.

19. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 19 Homework, Page 604 Determine f so that its graph contains the given points. 69.

20. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 20 Homework, Page 604 73.Children ride a train for 25 cents, adults pay $1.00, and seniors pay 75 cents. On a given day, 1400 passengers paid $740 for their rides. There were 250 more children than all other passengers. Find the number of children, adults, and senior riders.

21. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 21 Homework, Page 604 77.Morgan has $50,000 to invest and wants to receive $5,000 interest the first year. He puts part in CDs earning 5.75% APY, part in bonds earning 8.7% APY, and the rest in a growth fund earning 14.6% APY. How much should he put in each fund if he puts the least amount possible in the growth fund.

22. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 22 Homework, Page 604 Use inverse matrices to find the equilibrium point for the supply and demand curves. 81.

23. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 7.4 Partial Fractions

24. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 24 What you’ll learn about Partial Fraction Decomposition Denominators with Linear Factors Denominators with Irreducible Quadratic Factors Applications … and why Partial fraction decompositions are used in calculus in integration and can be used to guide the sketch of the graph of a rational function.

25. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 25 Partial Fraction Decomposition of f(x)/d(x)

26. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 26 Example Decomposing a Fraction with Distinct Linear Factors

27. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 27 Example Decomposing a Fraction with Repeated Linear Factors

28. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 28 Example Decomposing a Fraction with an Irreducible Quadratic Factor

29. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 29 Example Reversing a Decomposed Fraction to Identify the Parent Function

30. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 30 Homework Homework Assignment #12 Read Section 7.5 Page 614, Exercises: 1 – 49 (EOO), skip 45

31. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 7.5 Systems of Inequalities in Two Variables

32. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 32 Quick Review

33. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 33 Quick Review Solutions

34. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 34 What you’ll learn about Graph of an Inequality Systems of Inequalities Linear Programming … and why Linear programming is used in business and industry to maximize profits, minimize costs, and to help management make decisions.

35. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 35 Steps for Drawing the Graph of an Inequality in Two Variables 1. Draw the graph of the equation obtained by replacing the inequality sign by an equal sign. Use a dashed line if the inequality is. Use a solid line if the inequality is ≤ or ≥. 2. Check a point in each of the two regions of the plane determined by the graph of the equation. If the point satisfies the inequality, then shade the region containing the point.

36. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 36 Example Graphing a Linear Inequality

37. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 37 Example Solving a System of Inequalities Graphically

38. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 38 Example Solving a Word Problem 38.Paul’s diet is to contain at least 24 units of carbohydrates and 16 units of protein. Food substance A costs $1.40 per unit and each unit contains 3 units of carbohydrates and 4 units of protein. Food substance B costs $0.90 per unit and each unit contains 2 units of carbohydrates and 1 units of protein. How many units of each food substance should be purchased to minimize cost? What is the minimum cost?