Systems of Equations and Matrices Active Learning Lecture Slides For use with Classroom Response Systems Chapter 6 Systems of Equations and Matrices © 2009 Pearson Education, Inc.

CHAPTER 6: Systems of Equations and Matrices 6.1 Systems of Equations in Two Variables 6.2 Systems of Equations in Three Variables 6.3 Matrices and Systems of Equations 6.4 Matrix Operations 6.5 Inverses of Matrices 6.6 Determinants and Cramer’s Rule 6.7 Systems of Inequalities and Linear Programming 6.8 Partial Fractions Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. What is the x-coordinate when solving the system: a. 1 b. 4 c. 4 d. Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. What is the x-coordinate when solving the system: a. 1 b. 4 c. 4 d. Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. What is the y-coordinate when solving the system: a. b. c. d. Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. What is the y-coordinate when solving the system: a. b. c. d. Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Which graph is the solution to the system? a. b. c. d. Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Which graph is the solution to the system? a. b. c. d. Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. What is the solution to the system? a. (5, 0) b. (0, 0) c. no solution d. infinitely many solutions Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. What is the solution to the system? a. (5, 0) b. (0, 0) c. no solution d. infinitely many solutions Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. What is the solution to the system? a. (0, 1) b. (2, 0) c. no solution d. infinitely many solutions Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. What is the solution to the system? a. (0, 1) b. (2, 0) c. no solution d. infinitely many solutions Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. When solving the system, what is the z-coordinate? a. 2 b. 5 c. 3 d. 22 Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. When solving the system, what is the z-coordinate? a. 2 b. 5 c. 3 d. 22 Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. When solving the system, what is the z-coordinate? a. b. c. 5 d. Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. When solving the system, what is the z-coordinate? a. b. c. 5 d. Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. When solving the system, what is the y-coordinate? a. 3 b. 1 c. 2 d. 1 Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. When solving the system, what is the y-coordinate? a. 3 b. 1 c. 2 d. 1 Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. One summer 1280 tickets were sold for a children’s theatre production. The tickets cost $12 for children, $15 for adults, and $8 for seniors. The same number of children and senior tickets were sold. Total receipts were $14,350. How many adult tickets were sold? a. 250 b. 310 c. 500 d. 720 Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. One summer 1280 tickets were sold for a children’s theatre production. The tickets cost $12 for children, $15 for adults, and $8 for seniors. The same number of children and senior tickets were sold. Total receipts were $14,350. How many adult tickets were sold? a. 250 b. 310 c. 500 d. 720 Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. The local bakery sold 120 loaves of bread. The harvest grain bread cost $5 per loaf, the 7-grain bread cost $6 per loaf and the rustic loaf cost $7 per loaf. There were 15 fewer 7-grain loaves sold than harvest grain. Total receipts were $750. How many rustic loaves of bread were sold? a. 65 loaves b. 68 loaves c. 29 loaves d. 34 loaves Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. The local bakery sold 120 loaves of bread. The harvest grain bread cost $5 per loaf, the 7-grain bread cost $6 per loaf and the rustic loaf cost $7 per loaf. There were 15 fewer 7-grain loaves sold than harvest grain. Total receipts were $750. How many rustic loaves of bread were sold? a. 65 loaves b. 68 loaves c. 29 loaves d. 34 loaves Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find C + B. a. b. c. d. not here Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find C + B. a. b. c. d. not here Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find C – A. a. b. c. d. not possible Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find C – A. a. b. c. d. not possible Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find CB. a. b. c. d. not possible Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find CB. a. b. c. d. not possible Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find 2A. a. b. c. d. not possible Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find 2A. a. b. c. d. not possible Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find 2B + C. a. b. c. d. not here Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find 2B + C. a. b. c. d. not here Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find B-1. a. b. c. d. not possible Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find B-1. a. b. c. d. not possible Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find C-1. a. b. d. not possible c. Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find C-1. a. b. d. not possible c. Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find B-1. a. b. c. d. not possible Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find B-1. a. b. c. d. not possible Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Solve the system. a) (10, 3) b) (1, 4) c) (10, 14) d) (3, 6) Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Solve the system. a) (10, 3) b) (1, 4) c) (10, 14) d) (3, 6) Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Solve the system. a) (2, 3) b) (2, 6) c) (2, 6) d) (3, 2) Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Solve the system. a) (2, 3) b) (2, 6) c) (2, 6) d) (3, 2) Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find the determinant. a. 10 b. 2 c. 4 d. 2 Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find the determinant. a. 10 b. 2 c. 4 d. 2 Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find the determinant. a. 132 b. 128 c. 96 d. 60 Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find the determinant. a. 132 b. 128 c. 96 d. 60 Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find the determinant. a. 104 b. 8 c. 52 d. 78 Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find the determinant. a. 104 b. 8 c. 52 d. 78 Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find x using Cramer’s rule. a. b. c. d. Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find x using Cramer’s rule. a. b. c. d. Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find y using Cramer’s rule. a. b. c. d. Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find y using Cramer’s rule. a. b. c. d. Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Which of the following represents the graph of 5x  4y ≤ 10? a. b. c. d. Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Which of the following represents the graph of 5x  4y ≤ 10? a. b. c. d. Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Which of the following represents the graph of 3x – 4y ≤ 12? a. b. c. d. Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Which of the following represents the graph of 3x – 4y ≤ 12? a. b. c. d. Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Which of the following represents the graph of a. b. c. d. Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Which of the following represents the graph of a. b. c. d. Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. The Falls High School student council sells hot dogs and popcorn during movie intermissions. To earn a profit they must sell at least 20 popcorns but cannot sell more than 50. They must also sell at least 12 hot dogs but cannot cook more than 36. They cannot sell more than 60 items altogether. The profit on a hot dog is $1 and on a popcorn is $0.75. What is the maximum profit? a. $54 b. $48 c. $60 d. $73.50 Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. The Falls High School student council sells hot dogs and popcorn during movie intermissions. To earn a profit they must sell at least 20 popcorns but cannot sell more than 50. They must also sell at least 12 hot dogs but cannot cook more than 36. They cannot sell more than 60 items altogether. The profit on a hot dog is $1 and on a popcorn is $0.75. What is the maximum profit? a. $54 b. $48 c. $60 d. $73.50 Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Joanne’s Bakery prepares pies and cakes. In a given week, a maximum of 120 pies and cakes can be prepared, of which 60 pies and 40 cakes are required by regular customers. The profit on a pie is $5 and on a cake is $6. How many pies should the bakery make to maximize profit? a. 40 b. 50 c. 60 d. 70 Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Joanne’s Bakery prepares pies and cakes. In a given week, a maximum of 120 pies and cakes can be prepared, of which 60 pies and 40 cakes are required by regular customers. The profit on a pie is $5 and on a cake is $6. How many pies should the bakery make to maximize profit? a. 40 b. 50 c. 60 d. 70 Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find one of the partial fractions when is decomposed. a. b. c. d. Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find one of the partial fractions when is decomposed. a. b. c. d. Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find one of the partial fractions when is decomposed. a. b. c. d. Copyright © 2009 Pearson Education, Inc.

Copyright © 2009 Pearson Education, Inc. Find one of the partial fractions when is decomposed. a. b. c. d. Copyright © 2009 Pearson Education, Inc.