SOLUTION MANUAL
Finite Mathematics & Its Applications
13th Edition by Goldstein Chapters 1 - 12
, Contents
Chapter 1:
QWE Linear Equations and Straight Lines
QWE QWE QWE QWE 1–1
Chapter 2:
QWE Matrices 2–1
Chapter 3:
QWE Linear Programming, A Geometric Approach
QWE QWE QWE QWE 3–1
Chapter 4:
QWE The Simplex Method
QWE QWE 4–1
Chapter 5:
QWE Sets and Counting
QWE QWE 5–1
Chapter 6:
QWE Probability 6–1
Chapter 7:
QWE Probability and Statistics QWE QWE 7–1
Chapter 8:
QWE Markov Processes QWE 8–1
Chapter 9:
QWE The Theory of Games
QWE QWE QWE 9–1
Chapter10: The Mathematics of Finance
QWE QWE QWE QWE 10–1
Chapter 11: Logic
QWE 11–1
Chapter 12: DifferenceEquationsandMathematicalModels
QWE QWE QWE QWE QWE 12–1
, Chapter 1
QWE
Exercises 1.1 5
6. Left 1, down
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Q
Q W E QWE QWE Q W E
2
1. Right 2, up 3 QWE QWE QWE
y
y
(2, 3)
QWE
x
x
(–1, –52) Q W E QWE
QWE
7. Left 20, up 40
2. Left 1, up 4
Q W E QWE QWE QWE
QWE QWE QWE
y
y
(–20, 40)
(–1, 4)
QWE
QWE
x
x
8. Right 25, up 30
3. Down 2
Q W E QWE QWE QWE
Q W E QWE
y
y
(25, 30) QWE
x
x
(0, –2) QWE
9. Point Q is 2 units to the left and 2 units up or
4. Right 2
QWE QWE QWE QWE QWE QWE QWE QWE QWE QWE QWE QWE
QWE
y (—2,2). QWE
10. Point P is 3 units to the right and 2 units down or
QWE QWE QWE QWE QWE QWE QWE QWE QWE QWE QWE QWE
(3,—2).
x
(2, 0)
QWE
1
11. —2(1)+ (3) =—2+1 =—1so yes the point is
QWE
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3
on the line. QWE QWE
5. Left 2, up 1 1
12. —2(2)+ (6) =—1is false, so no the point is not
QWE
QWE QWE QWE
y QWE QWE QW E QWE QWE Q W E Q W E Q W E Q W E Q W E Q W E Q W E
3
on the line QWE QWE
(–2, 1)
x
QWE
Copyright © 2023 Pearson Education, Inc.
QWE QWE QWE QWE QWE 1-1
, Chapter 1: Linear Equations and Straight Lines QWE QWE QWE QWE QWE QWE ISM: Finite Math
QWE QWE
1 24. 0 = 5
Q W E QWE QWE
13. —2x+ y =—1 Substitute the x and y
Q W E
QWE QWE Q W E QWE Q W E Q W E Q W E Q W E Q W E
no solution
3
QWE
x-
coordinates of the point into the equation: QWE QWE QWE QWE QWE QWE
intercept: none Wh
f 1 ıh f h
' ,3 →—2 ' 1 ı +1(3)=—1→—1+1=—1 is
QWE QWE
en x = 0, y = 5y-
E
QW
E
QW E
QW
y' ı ' ı
QWE QW E QWE QW E QWE QW E E
QW
E
QW E
QW E
QW E
QW E
QW E
QW E
QW E
QW Q W E
E
QW
Q W E
intercept: (0, 5) QWE QWE
2 J y2J 3 QW E QW E
Q W E E
QW
a false statement. So no the point is not on theline.
QWE QWE QWE QWE QWE QWE QW E QW E QWE QWE E
QW
25. When y = 0, x = 7x-
QWE QWE QW E QWE QW E QWE QWE E
QW
f 1 h f1h intercept: (7, 0)0 = QWE QWE E
QW QWE QWE
—2 ' ı + ' ı(—1)=—1 is true so yes the point is QW
E E
QW Q W E QW E QWE QWE QWE QWE QW E
7
14. no solution QWE
'y3 ıJ 'y3 ıJ QWEQWE QWE
y-intercept:none QW
E
on the line. QWE QWE
26. 0 = –8x
Q W E QWE QWE
15. m = 5, b = 8 Q W E QWE QWE QWE QWE QWE
x=0 QWE QWE
x-intercept: (0, 0) QWE QWE
16. m = –2 and b = –6
Q W E QWE QWE QW E QWE QWE QWE
y = –8(0) QWE QWE
y=0 QWE QWE
17. Q W E y = 0x + 3; m = 0, b = 3
QWE QWE QWE QWE QW E QWE QWE QWE QWE QWE
y-intercept: (0, 0) QWE QWE
2 2 1
27. 0 = x –1
Q W E
y = x+0; m= , b=0
QW E E
QW
18.
QWE QW E QW E QWE
3
QWE QWE E
QW E
QW Q W E QWE QW E QWE QWE E
QW
3 3
x =3 QWE QWE
19. 14x+7y =21 x-intercept: (3, 0) QWE QWE
1
Q W E E
QW E
QW E
QW QWE E
QW
y = (0) –1
QWE
7y =—14x+21 QWE QW E QWE QWE QWE
Q W E QW E QW E QWE
3
y =—2x+3 Q W E QWE QWE QWE
y = –1 QWE QWE
y-intercept: (0, –1)
20. x—y =3
QWE QWE
QWE QWE QW E QWE
y
—y =—x+3 QW E QWE QWE QWE
y = x—3 QW E QW E QWE QWE
(3, 0) QWE
21. 3x =5
QWEQWEQ W E QWE E
QW
x
5 (0, –1) QWE
x= QWE QW
E
3
1 2 28. When x = 0, y = 0.
– x + y =10
QWE QWE QWE QWE QWE QWE
22. 2 3
QWE Q W E QWE
When x = 1, y = 2. QWE QWE QWE QWE QWE QWE
2 1 y
y = x+10
Q W E Q W E
QW E Q W E QWE
3 2
3
y = x+15
Q W E
QW E Q W E QWE
(1, 2) QWE
4 x
(0, 0) QWE
23. 0 =—4x +8 QW E QWE QWE QWE
4x =8 Q W E QWE
x =2 QW E QWE
x-intercept: (2, 0) QWE QWE
y = –4(0) + 8 QWE QWE QW E QWE
y=8 QWE QWE
y-intercept: (0, 8) QWE QWE
1-2 Copyright © 2023 Pearson Education, Inc. QWE QWE QWE QWE QWE
Finite Mathematics & Its Applications
13th Edition by Goldstein Chapters 1 - 12
, Contents
Chapter 1:
QWE Linear Equations and Straight Lines
QWE QWE QWE QWE 1–1
Chapter 2:
QWE Matrices 2–1
Chapter 3:
QWE Linear Programming, A Geometric Approach
QWE QWE QWE QWE 3–1
Chapter 4:
QWE The Simplex Method
QWE QWE 4–1
Chapter 5:
QWE Sets and Counting
QWE QWE 5–1
Chapter 6:
QWE Probability 6–1
Chapter 7:
QWE Probability and Statistics QWE QWE 7–1
Chapter 8:
QWE Markov Processes QWE 8–1
Chapter 9:
QWE The Theory of Games
QWE QWE QWE 9–1
Chapter10: The Mathematics of Finance
QWE QWE QWE QWE 10–1
Chapter 11: Logic
QWE 11–1
Chapter 12: DifferenceEquationsandMathematicalModels
QWE QWE QWE QWE QWE 12–1
, Chapter 1
QWE
Exercises 1.1 5
6. Left 1, down
WE
Q
Q W E QWE QWE Q W E
2
1. Right 2, up 3 QWE QWE QWE
y
y
(2, 3)
QWE
x
x
(–1, –52) Q W E QWE
QWE
7. Left 20, up 40
2. Left 1, up 4
Q W E QWE QWE QWE
QWE QWE QWE
y
y
(–20, 40)
(–1, 4)
QWE
QWE
x
x
8. Right 25, up 30
3. Down 2
Q W E QWE QWE QWE
Q W E QWE
y
y
(25, 30) QWE
x
x
(0, –2) QWE
9. Point Q is 2 units to the left and 2 units up or
4. Right 2
QWE QWE QWE QWE QWE QWE QWE QWE QWE QWE QWE QWE
QWE
y (—2,2). QWE
10. Point P is 3 units to the right and 2 units down or
QWE QWE QWE QWE QWE QWE QWE QWE QWE QWE QWE QWE
(3,—2).
x
(2, 0)
QWE
1
11. —2(1)+ (3) =—2+1 =—1so yes the point is
QWE
QWE EQW QW E QWE QWE QWE QWE Q W E Q W E Q W E Q W E
3
on the line. QWE QWE
5. Left 2, up 1 1
12. —2(2)+ (6) =—1is false, so no the point is not
QWE
QWE QWE QWE
y QWE QWE QW E QWE QWE Q W E Q W E Q W E Q W E Q W E Q W E Q W E
3
on the line QWE QWE
(–2, 1)
x
QWE
Copyright © 2023 Pearson Education, Inc.
QWE QWE QWE QWE QWE 1-1
, Chapter 1: Linear Equations and Straight Lines QWE QWE QWE QWE QWE QWE ISM: Finite Math
QWE QWE
1 24. 0 = 5
Q W E QWE QWE
13. —2x+ y =—1 Substitute the x and y
Q W E
QWE QWE Q W E QWE Q W E Q W E Q W E Q W E Q W E
no solution
3
QWE
x-
coordinates of the point into the equation: QWE QWE QWE QWE QWE QWE
intercept: none Wh
f 1 ıh f h
' ,3 →—2 ' 1 ı +1(3)=—1→—1+1=—1 is
QWE QWE
en x = 0, y = 5y-
E
QW
E
QW E
QW
y' ı ' ı
QWE QW E QWE QW E QWE QW E E
QW
E
QW E
QW E
QW E
QW E
QW E
QW E
QW E
QW Q W E
E
QW
Q W E
intercept: (0, 5) QWE QWE
2 J y2J 3 QW E QW E
Q W E E
QW
a false statement. So no the point is not on theline.
QWE QWE QWE QWE QWE QWE QW E QW E QWE QWE E
QW
25. When y = 0, x = 7x-
QWE QWE QW E QWE QW E QWE QWE E
QW
f 1 h f1h intercept: (7, 0)0 = QWE QWE E
QW QWE QWE
—2 ' ı + ' ı(—1)=—1 is true so yes the point is QW
E E
QW Q W E QW E QWE QWE QWE QWE QW E
7
14. no solution QWE
'y3 ıJ 'y3 ıJ QWEQWE QWE
y-intercept:none QW
E
on the line. QWE QWE
26. 0 = –8x
Q W E QWE QWE
15. m = 5, b = 8 Q W E QWE QWE QWE QWE QWE
x=0 QWE QWE
x-intercept: (0, 0) QWE QWE
16. m = –2 and b = –6
Q W E QWE QWE QW E QWE QWE QWE
y = –8(0) QWE QWE
y=0 QWE QWE
17. Q W E y = 0x + 3; m = 0, b = 3
QWE QWE QWE QWE QW E QWE QWE QWE QWE QWE
y-intercept: (0, 0) QWE QWE
2 2 1
27. 0 = x –1
Q W E
y = x+0; m= , b=0
QW E E
QW
18.
QWE QW E QW E QWE
3
QWE QWE E
QW E
QW Q W E QWE QW E QWE QWE E
QW
3 3
x =3 QWE QWE
19. 14x+7y =21 x-intercept: (3, 0) QWE QWE
1
Q W E E
QW E
QW E
QW QWE E
QW
y = (0) –1
QWE
7y =—14x+21 QWE QW E QWE QWE QWE
Q W E QW E QW E QWE
3
y =—2x+3 Q W E QWE QWE QWE
y = –1 QWE QWE
y-intercept: (0, –1)
20. x—y =3
QWE QWE
QWE QWE QW E QWE
y
—y =—x+3 QW E QWE QWE QWE
y = x—3 QW E QW E QWE QWE
(3, 0) QWE
21. 3x =5
QWEQWEQ W E QWE E
QW
x
5 (0, –1) QWE
x= QWE QW
E
3
1 2 28. When x = 0, y = 0.
– x + y =10
QWE QWE QWE QWE QWE QWE
22. 2 3
QWE Q W E QWE
When x = 1, y = 2. QWE QWE QWE QWE QWE QWE
2 1 y
y = x+10
Q W E Q W E
QW E Q W E QWE
3 2
3
y = x+15
Q W E
QW E Q W E QWE
(1, 2) QWE
4 x
(0, 0) QWE
23. 0 =—4x +8 QW E QWE QWE QWE
4x =8 Q W E QWE
x =2 QW E QWE
x-intercept: (2, 0) QWE QWE
y = –4(0) + 8 QWE QWE QW E QWE
y=8 QWE QWE
y-intercept: (0, 8) QWE QWE
1-2 Copyright © 2023 Pearson Education, Inc. QWE QWE QWE QWE QWE
