Finite Mathematics & Its Applications – 13th Edition by Goldstein | Complete Solution Manual Chapters 1–12

SOLUTION MANUA
Finite Mathematics & Its Application
13th Edition by Goldstein Chapters 1 - 1

, Contents
Chapter 1:
ji Linear Equations and Straight Lines
ji ji ji ji 1–1
Chapter 2:
ji Matrices 2–1

Chapter 3:
ji Linear Programming, A Geometric Approach
ji ji ji ji 3–1

Chapter 4:
ji The Simplex Method
ji ji 4–1

Chapter 5:
ji Sets and Counting
ji ji 5–1

Chapter 6:
ji Probability 6–1

Chapter 7:
ji Probability and Statistics
ji ji 7–1

Chapter 8:
ji Markov Processes ji 8–1

Chapter 9:
ji The Theory of Games
ji ji ji 9–1

Chapter 10: The Mathematics of Finance
ji ji ji ji 10–1

Chapter 11: Logic
ji 11–1

Chapter 12: Difference Equations and Mathematical Models
ji ji ji ji ji 12–1

, Chapter 1
ji




Exercises 1.1
ji 5
6. Left 1, down
j i ji ji j i


2
1. Right 2, up 3 ji ji ji
y
y


(2, 3)
ji


x
x
(–1, – 52) ji ji
ji




7. Left 20, up 40
2. Left 1, up 4
j i ji ji ji

ji ji ji
y
y

(–20, 40)
(–1, 4)
ji
ji




x
x




8. Right 25, up 30
j i ji ji ji

3. Down 2
j i ji
y
y


(25, 30) ji




x
x
(0, –2) ji




9. Point Q is 2 units to the left and 2 units up or
4. Right 2
ji ji ji ji ji ji ji ji ji ji ji ji
ji


y (—2,2). ji




10. Point P is 3 units to the right and 2 units down or
ji ji ji ji ji ji ji ji ji ji ji ji



(3,—2).
x
(2, 0)
ji 1 ji

11. —2(1)+ (3) =—2+1=—1so yes the point is ji ji ji ji ji ji ji ji ji ji ji


3
on the line. ji ji




5. Left 2, up 1 1 ji

12. —2(2)+ (6) =—1is false, so no the point is not
ji ji ji


y ji ji ji ji ji ji ji ji ji ji ji ji


3
on the line ji ji




(–2, 1) ji
x




Copyright © 2023 Pearson Education, Inc.
ji ji ji ji ji 1-1

, Chapter 1: Linear Equations and Straight Lines
ji ji ji ji ji ji ISM: Finite Math
ji ji




1 ji
24. 0 = 5
j i ji ji


13. —2x + y =—1 Substitute the x and y ji ji ji ji j i ji ji ji ji
no solution ji

3 x-
coordinates of the point into the equation: ji ji ji ji ji ji
intercept: none Wh
f 1 hı f h
ji ji


' ,3 →—2 ' 1 ı +1(3)=—1→—1+1=—1 is
ji
ji ji
en x = 0, y = 5y- ji ji ji ji ji ji ji

y' ı ' ı
ji ji ji ji ji ji ji ji ji j i

ji
intercept: (0, 5) ji ji


2 J y2J 3 jijij i ji


a false statement. So no the point is not on theline.
ji ji ji ji ji ji ji ji ji ji ji 25. When y = 0, x = 7x-
ji ji ji ji ji ji ji ji




f 1h f1h intercept: (7, 0)0 = ji ji ji ji ji



—2 ' ı + ' ı(—1) =—1 is true so yes the point is ji ji j i ji ji ji ji ji ji 7
14. no solution ji


'y3 ıJ 'y3 Jı jijiji
y-intercept: none ji




on the line. ji ji
26. 0 = –8x
j i ji ji




15. m = 5, b = 8
j i ji ji ji ji ji
x=0 ji ji



x-intercept: (0, 0) ji ji



16. m = –2 and b = –6
j i ji ji ji ji ji ji
y = –8(0)ji ji


y=0 ji ji



17. y = 0x + 3; m = 0, b = 3
j i ji ji ji ji ji ji ji ji ji ji y-intercept: (0, 0) ji ji




2 2 1 ji


18. y = x+0; m = , b =0
ji ji
ji

ji ji ji ji ji
ji

ji ji ji
27. 0 = x –1 ji ji ji ji



3 3 3
x=3 ji ji




19. 14x+7y =21
j i ji ji ji ji ji
x-intercept: (3, 0) ji ji


1 ji

7y =—14x+21 ji ji ji ji ji
y = (0) –1 ji ji ji ji


3
y =—2x +3
ji ji ji ji
y = –1 ji ji



y-intercept: (0, –1)
20. x—y =3
ji ji

ji ji ji ji y
—y =—x +3 ji ji ji ji




y = x —3 ji ji ji ji


(3, 0) ji

21. 3x =5
jijij i ji ji
x
5 (0, –1) ji


x= ji ji


3
1 2 28. When x = 0, y = 0. ji ji ji ji ji ji


22. – x + y = 10 ji ji ji

2 3 When x = 1, y = 2. ji ji ji ji ji ji


2 1 ji ji y
y = x +10 ji ji ji


3 2
3 ji

y = x +15 ji ji ji
(1, 2) ji

4 x
(0, 0) ji



23. 0 =—4x +8 ji ji ji ji




4x = 8 ji ji



x =2 ji ji


x-intercept: (2, 0) ji ji


y = –4(0) + 8
ji ji ji ji


y=8
ji ji


y-intercept: (0, 8) ji ji




1-2 Copyright © 2023 Pearson Education, Inc. ji ji ji ji ji