slide 8 - 1 copyright © 2009 pearson education, inc. active learning lecture slides for use with...

1Copyright © 2009 Pearson Education, Inc.

Active Learning Lecture SlidesFor use with Classroom Response Systems

© 2009 Pearson Education, Inc.All rights reserved.

Chapter 8Systems of

Equations and Inequalities


Solve the system of equations by substitution.

a.

b.

c.

d.

x 12, y 2; 12, 2

x 2, y3; 2, 3

x 7y 2

3x y34

x 3, y7; 3, 7

x 7, y12; 7,12


Solve the system of equations by elimination.

a.

b.

c.

d.

x 10, y10; 10,10

x 0, y10; 0,10

5x 3y80

2x y30

x 10, y0; 10,0

x 0, y0; 0,0


Solve the system of equations.

a.

b.

c.

d. inconsistent

x 7, y9; 7,9

x 4, y3; 4, 3

7x 3y9

28x 12y 27

x 7

6, y

1

2;

7

6,

1

2



a.

b.

c.

d. inconsistent

x 7, y9; 7,9

x 4, y3; 4, 3

7x 3y9

28x 12y 27

x 7

6, y

1

2;

7

6,

1

2



a.

b.

c.

d. inconsistent

or y3

4x 3, where x is any real number

x 0, y0; 0,0

4 3

4 16 12

x y

x y

x 3, y0; 3,0

x, y yx

4 3, where x is any real number



a.

b.

c.

d. inconsistent

or y3

4x 3, where x is any real number

x 0, y0; 0,0

x 3, y0; 3,0

x, y yx

4 3, where x is any real number

4 3

4 16 12

x y

x y



a.

b.

c.

d. inconsistent

x 3, y 4, z 1; 3, 4,1

x 4, y1, z 3; 4,1, 3

5x 5y z 16

2x 2y z 8

5x y 5z 4

x 3, y1, z 4; 3,1, 4


Write the augmented matrix of the system of equations.

a.

c.

9 2 5

6 5 8

2 5 5

5

17

16

b.

d.

9x 6y 2z 5

2x 5y 5z 17

5x 8y 5z 16

9 6 2

2 5 5

5 8 5

5

17

16

9 6

2 5

5 8

2

5

5

5 2 6

17 5 5

16 5 8

9

2

5


Write the system of equations corresponding to the augmented matrix.

a.

c.

4x 7y 7z 2

9x 5z 4

9x 3y 2

b.

d.

4 7 7

9 0 5

9 3 0

2

4

2

4x 7y 7z 2

9x 5z 4

9x 3z 2

4x 7y 7z 2

9x 5z 4

9x 3y 2

4x 7y 7z 2

9x 5z 4

9x 3z 2


Performthe row operations.

a.

c.

1 3 5

0 7 16

0 18 30

2

13

23

b.

d.

(a) R2 4r1 r2(b) R3 2r1 r3(c) R3 6r2 r3

1 3 5

0 7 16

0 53 110

2

13

88

1 3 5

0 8 9

0 37 40

2

3

8

1 3 5

0 17 24

0 113 158

2

7

52

1 3 5

4 5 4

2 5 4

2

5

6


Solve the system of equations using Cramer’s Rule.

a.

b.

c.

d.

x 3, y 5; 3, 5

x 5, y 3; 5, 3

x 5, y 3; 5, 3

x 3, y5; 3,5

6x 2y 8

4x y 7


Find the value of the determinant.

a. 62

b. –70

c. –62

d. –192

5 1 2

1 5 4

1 3 5


Find the value of the determinant second determinant.

a. 52

b. –52

c. 0

d. cannot be determined

x y z

u v w

1 2 3

52

1 2 3

u v w

x y z

?


Find A – B.a.

c. 5 10 7

13 1 2

3 3 8

5 10 7

13 1 8

3 3 2

9 2 9

1 9 2

3 15 4

9 2 9

1 9 4

3 15 2

b.

d.

Let A7 4 8

6 5 1

0 6 3

and B 2 6 1

7 4 3

3 9 5

.


Find 3A.

a.

c. 0 7

3 5

9 4

0 2

9 12

0 6

9 12

0 2

b.

d.

Let A 3 4

0 2

.


Compute the product.

a.

c. 3 3 0

0 0 25

2 0

25 6

0 2

6 25

b.

d. Not defined

1 3 1

2 0 5

3 0

1 1

0 5


b.

d.

The matrix is nonsingular. Find the inverse of the matrix.

a.

c. 1 1 1

2 3 0

0 2 1

1 3 1

0 2 1

2 3 0

1 1 0

2 3 0

0 2 1

3 3 1

2 2 1

4 5 2

1 1 1

0 2 1

2 3 0


b.

d.

Write the partial fraction decomposition.

a.

c. 5

x 3

4

x 5

4

x 3

5

x 5

4

x 3

5

x 5

x 13

x 3 x 5

5

x 3

4

x 5


b.

d.


a.

c. 5

x 3

4

x 5

4

x 3

5

x 5

4

x 3

5

x 5

x 13

x 3 x 5

5

x 3

4

x 5


b.

d.


a.

c. 2

x 2

1

x 1

2

x 1 2

2

x 2

1

x 1

2

x 1 2

2

x 2

1

x 1

2

x 1 2

3x2 9x 8

x 2 x 1 2

2

x 2

1

x 1

2

x 1 2


b.

d.


a.

c. 5

x 1

5x 2

x2 x 1

5

x 1

5x 2

x2 x 1

5

x 1

5

x 1

2

x 1

12x 3

x 1 x2 x 1

5

x 1

2x 5

x2 x 1


b.

d.


a.

c. 3x 3

x2 5

15x 15

x2 5 2

3x 3

x2 5

15x 15

x2 5 2

3x 3

x2 5

15x 15

x2 5 2

3x3 3x2

x2 5 2

3x 3

x2 5

15x 15

x2 5 2


b.

d.

Solve the system of equations using substitution.

a.

c. x 5, y6

x 6, y5

( 5,6), 6,5

x 5, y 6

x 6, y 5

(5, 6), 6, 5

x 5, y6

x 6, y5

(5,6), 6,5

xy30

x y 11

x 5, y 6

x 6, y 5

( 5, 6), 6, 5


The sum of the squares of two numbers is 65. The sum of the two numbers is 3. Find the two numbers.

a. –4 and 7 or –7 and 4

b. –4 and 7

c. –7 and 4

d. 4 and 7 or –7 and –4


Graph

a.

3x 4y12.

b.

c. d.


Graph the solution set of

a.

x 2y 6

3x 2y 18

.

b.

c. d.


Mrs. Jones needs 7 hours to knit a hat and 3 for an afghan. She has no more than 46 hours, enough material for no more than 10 items and needs at least two afghans. Write a system of inequalities that describes these constraints.

a.

c.

7x 3y46

x y10

y2

b.

d.7x 3y46

x y10

x 2

7x 3y46

x y10

x 2

7x 3y46

x y10

y2


A candy company has 145 pounds of cashews and 190 pounds of peanuts. The deluxe mix contains half cashews and half peanuts and sells for $8 per pound. The economy mix has one third cashews and two thirds peanuts and sells for $5.70 per pound. How many pounds of each mix should be prepared for maximum revenue?

a. 100 deluxe,45 economy

c. 200 deluxe,135 economy

b. 300 deluxe,90 economy

d. 145 deluxe,0 economy

slide 8 - 1 copyright © 2009 pearson education, inc. active learning lecture slides for use with...

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