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

SOLUTION MANUAL
Finite Mathematics & Its Applications
13th Edition by Goldstein Chapters 1 - 12

, Contents
Chapter1:
qf LinearEquationsandStraightLines
qf qf qf qf 1–1
Chapter2:
qf Matrices 2–1

Chapter3:
qf Linear Programming, A Geometric Approach
fq fq fq fq 3–1

Chapter4:
qf TheSimplexMethod
qf qf 4–1

Chapter5:
qf SetsandCounting
qf qf 5–1

Chapter 6:
fq Probability 6–1

Chapter7:
qf Probabilityand Statistics qf fq 7–1

Chapter8:
qf MarkovProcesses qf 8–1

Chapter9:
qf The Theory ofGames
fq fq qf 9–1

Chapter10: TheMathematicsofFinance
qf qf qf qf 10–1

Chapter11: Logic
qf 11–1

Chapter12: DifferenceEquationsandMathematicalModels
qf qf qf qf qf 12–1

, Chapter1
fq




Exercises1.1 5
6. Left 1, down
fq




f q fq fq f q




2
1. Right 2, up 3 fq fq fq

y
y


(2, 3)
fq




x
x
(–1, –52) f q qf
qf




7. Left 20, up 40
2. Left 1, up 4
f q fq fq fq




fq fq fq


y
y

(–20, 40)
(–1, 4)
fq



fq




x
x




8. Right 25, up 30
3. Down 2
f q fq fq fq




f q fq


y
y


(25, 30) fq




x
x
(0, –2) fq




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




fq




y (—2,2). qf




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




(3,—2).
x
(2, 0)
fq
1
11. —2(1)+ (3) =—2+1=—1so yes the point is
qf




qf qf fq qf qf qf qf f q f q f q f q




3
on the line. fq fq




5. Left 2, up 1 1
12. —2(2)+ (6) =—1is false, so no the point is not
qf
fq fq fq




y qf qf fq qf qf f q f q f q f q f q f q f q




3
on the line fq fq




(–2, 1)
x
fq




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

, Chapter 1: Linear Equations and Straight Lines fq fq fq q
f fq fq ISM: Finite Math
fq fq




1 24. 0 = 5
f q fq fq




13. —2x + y =—1 Substitute the x and y
f q




fq qf fq qf f q f q f q f q f q


no solution
3
fq




x-
coordinatesof the point into the equation: qf qf fq fq fq fq


intercept: none Wh
f 1 ıh f h
' ,3 →—2 ' 1 ı +1(3)=—1→—1+1=—1 is
fq fq




en x = 0, y = 5y-
qf
qf qf




y' ı 'ı
fq fq fq fq fq fq qf
qf qf qf qf qf qf qf qf f q
qf




f q
intercept:(0, 5) qf fq




2J y2J 3 fqf qf
q qf




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




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




—2 ' ı + ' ı(—1)=—1 is true so yes the point is qf qf f q fq fq fq fq fq fq
7
14. no solution fq




'y3 ıJ 'y3 ıJ fqfqfq
y-intercept:none qf




on the line. fq fq


26. 0 = –8x
f q fq fq




15. m = 5, b = 8 f q fq fq fq fq fq
x=0 fq fq




x-intercept: (0,0) fq qf




16. m = –2 and b = –6
f q fq fq fq fq fq fq
y = –8(0) fq fq




y=0 fq fq




17. y = 0x + 3; m = 0, b = 3
f q fq fq fq fq fq fq fq fq fq fq
y-intercept: (0,0) fq qf




2 2 1
27. 0 = x –1
fq




18. y = x+0; m= , b=0
fq qf

qf fq fq qf




3
fq fq fq qf f q fq fq fq fq qf




3 3
x =3 fq fq




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




1
f q fq qf qf fq qf




y = (0) –1
fq




7y =—14x+21 qf fq qf fq qf
f q fq fq qf




3
y =—2x+3 f q qf fq qf



y = –1 fq fq




y-intercept:(0,–1)
20. x—y =3
qf qf




fq qf fq qf
y
—y =—x+3 fq qf fq qf




y = x —3 fq fq fq qf




(3, 0) fq




21. 3x=5
fqfqf q fq qf
x
5 (0, –1) fq




x= fq qf




3
1 2 28. When x = 0, y = 0.
– x + y =10
fq fq fq fq fq fq




22. 2 3
fq f q qf




When x = 1, y = 2. fq fq fq fq fq fq




2 1 y
y = x+10
f q f q




fq f q fq




3 2
3
y = x+15
f q




fq f q fq

(1, 2) fq




4 x
(0, 0) fq




23. 0 =—4x+8 fq qf fq qf




4x =8 f q qf




x =2 fq qf




x-intercept: (2,0) fq qf




y = –4(0) + 8
fq fq fq fq




y=8 fq fq




y-intercept: (0,8) fq qf




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