SOLUTION MANUAL
Finite Mathematics & Its Applications
13th Edition by Goldstein Chapters 1 - 12
, Contents
Chapter 1:
i Linear Equations and Straight Lines
i i i i 1–1
Chapter 2:
i Matrices 2–1
Chapter 3:
i Linear Programming, A Geometric Approach
i i i i 3–1
Chapter 4:
i The Simplex Method
i i 4–1
Chapter 5:
i Sets and Counting
i i 5–1
Chapter 6:
i Probability 6–1
Chapter 7:
i Probability and Statistics
i i 7–1
Chapter 8:
i Markov Processesi 8–1
Chapter 9:
i The Theory of Games
i i i 9–1
Chapter 10: The Mathematics of Finance
i i i i 10–1
Chapter 11: Logic
i 11–1
Chapter 12: Difference Equations and Mathematical Models
i i i i i 12–1
, Chapter 1 i
Exercisesi1.1 5
6.i Lefti1,idowni
2
1. Righti2,iupi3 y
y
(2,i3)
x
x
(–1,i –i52i)
7.i Lefti20,iupi40
2. Lefti1,iupi4 y
y
(–20,i40)
(–1,i4)
x
x
8.i Righti25,iupi30
3.i Downi2 y
y
(25,i30)
x
x
(0,i–2)
9. PointiQiisi2iunitsitoitheileftiandi2iunitsiupior
4. Righti2
y (—2,i2).
10. PointiPiisi3iunitsitoitheirightiandi2iunitsidownior
(3,—2).
x
(2,i0) 1i
11. —2(1)i+i (3)i=i—2i+1i=i—1soi yesi thei pointi is
3
onitheiline.
5. Lefti2,iupi1 1i
y 12. —2(2)i+i (6)i=i—1iisi false,i soi noi thei pointi isi not
3
onitheiline
(–2,i1)
x
Copyrighti©i2023iPearsoniEducation,iInc. 1-1
, Chapteri1:iLineariEquationsiandiStraightiLines ISM:iFiniteiMath
1i 24.i 0i=i5
13. —2xi+i yi =i—1i Substitutei thei xi andi y noisolution
3 x-
coordinatesiofitheipointiintoitheiequation: intercept:inoneiWh
f 1i ıhi f h
' ,i3 →i—2 ' 1 ı +1i i(3)i=i—1i→i—1+1i=i—1i is enixi=i0,iyi=i5iy-
y' ı 'i ı intercept:i(0,i5)
2iii J yi2J 3
aifalseistatement.iSoinoitheipointiisinotionitheiline. 25.iWheniyi=i0,ixi=i7ix-
f 1 h f1h intercept:i(7,i0)i0i=i
—2 ' ı + ' ı(—1)i=i—1i isitrueisoiyesitheipointiis 7
14. noisolution
'y3 ıJiii'y3 ıJ y-intercept:inone
onitheiline. 26.i 0i=i–8x
15.i mi=i5,ibi=i8 xi=i0
x-intercept:i(0,i0)
16.i mi=i–2iandibi=i–6 yi=i–8(0)
yi=i0
17.i yi=i0xi+i3;imi=i0,ibi=i3 y-intercept:i(0,i0)
2i 2i 1i
18. yi=i xi+i0;i mi=i ,i bi=i0 27. 0i=i xi–i1
3 3 3
xi=i3
19.i 14xi+i7iyi=i21 x-intercept:i(3,i0)
1i
7iyi=i—14xi+i21 yi =i (0)i–i1
3
yi =i—2xi+i3 yi=i–1
y-intercept:i(0,i–1)
20. xi—iyi=i3 y
—yi =i—xi+i3
yi =ixi—i3
(3,i0)
21.iii 3xi=i5 x
5 (0,i–1)
xi=i
3
1 2 28. Whenixi=i0,iyi=i0.
22. – xi+ yi =i10
2 3 Whenixi=i1,iyi=i2.
2i 1i y
yi =i xi+10
3 2
3i
yi =i xi+15 (1,i2)
4 x
(0,i0)
23. 0i=i—4xi+i8
4xi =i8
xi=i2
x-intercept:i(2,i0)
yi=i–4(0)i+i8
yi=i8
y-intercept:i(0,i8)
1-2 Copyrighti©i2023iPearsoniEducation,iInc.
Finite Mathematics & Its Applications
13th Edition by Goldstein Chapters 1 - 12
, Contents
Chapter 1:
i Linear Equations and Straight Lines
i i i i 1–1
Chapter 2:
i Matrices 2–1
Chapter 3:
i Linear Programming, A Geometric Approach
i i i i 3–1
Chapter 4:
i The Simplex Method
i i 4–1
Chapter 5:
i Sets and Counting
i i 5–1
Chapter 6:
i Probability 6–1
Chapter 7:
i Probability and Statistics
i i 7–1
Chapter 8:
i Markov Processesi 8–1
Chapter 9:
i The Theory of Games
i i i 9–1
Chapter 10: The Mathematics of Finance
i i i i 10–1
Chapter 11: Logic
i 11–1
Chapter 12: Difference Equations and Mathematical Models
i i i i i 12–1
, Chapter 1 i
Exercisesi1.1 5
6.i Lefti1,idowni
2
1. Righti2,iupi3 y
y
(2,i3)
x
x
(–1,i –i52i)
7.i Lefti20,iupi40
2. Lefti1,iupi4 y
y
(–20,i40)
(–1,i4)
x
x
8.i Righti25,iupi30
3.i Downi2 y
y
(25,i30)
x
x
(0,i–2)
9. PointiQiisi2iunitsitoitheileftiandi2iunitsiupior
4. Righti2
y (—2,i2).
10. PointiPiisi3iunitsitoitheirightiandi2iunitsidownior
(3,—2).
x
(2,i0) 1i
11. —2(1)i+i (3)i=i—2i+1i=i—1soi yesi thei pointi is
3
onitheiline.
5. Lefti2,iupi1 1i
y 12. —2(2)i+i (6)i=i—1iisi false,i soi noi thei pointi isi not
3
onitheiline
(–2,i1)
x
Copyrighti©i2023iPearsoniEducation,iInc. 1-1
, Chapteri1:iLineariEquationsiandiStraightiLines ISM:iFiniteiMath
1i 24.i 0i=i5
13. —2xi+i yi =i—1i Substitutei thei xi andi y noisolution
3 x-
coordinatesiofitheipointiintoitheiequation: intercept:inoneiWh
f 1i ıhi f h
' ,i3 →i—2 ' 1 ı +1i i(3)i=i—1i→i—1+1i=i—1i is enixi=i0,iyi=i5iy-
y' ı 'i ı intercept:i(0,i5)
2iii J yi2J 3
aifalseistatement.iSoinoitheipointiisinotionitheiline. 25.iWheniyi=i0,ixi=i7ix-
f 1 h f1h intercept:i(7,i0)i0i=i
—2 ' ı + ' ı(—1)i=i—1i isitrueisoiyesitheipointiis 7
14. noisolution
'y3 ıJiii'y3 ıJ y-intercept:inone
onitheiline. 26.i 0i=i–8x
15.i mi=i5,ibi=i8 xi=i0
x-intercept:i(0,i0)
16.i mi=i–2iandibi=i–6 yi=i–8(0)
yi=i0
17.i yi=i0xi+i3;imi=i0,ibi=i3 y-intercept:i(0,i0)
2i 2i 1i
18. yi=i xi+i0;i mi=i ,i bi=i0 27. 0i=i xi–i1
3 3 3
xi=i3
19.i 14xi+i7iyi=i21 x-intercept:i(3,i0)
1i
7iyi=i—14xi+i21 yi =i (0)i–i1
3
yi =i—2xi+i3 yi=i–1
y-intercept:i(0,i–1)
20. xi—iyi=i3 y
—yi =i—xi+i3
yi =ixi—i3
(3,i0)
21.iii 3xi=i5 x
5 (0,i–1)
xi=i
3
1 2 28. Whenixi=i0,iyi=i0.
22. – xi+ yi =i10
2 3 Whenixi=i1,iyi=i2.
2i 1i y
yi =i xi+10
3 2
3i
yi =i xi+15 (1,i2)
4 x
(0,i0)
23. 0i=i—4xi+i8
4xi =i8
xi=i2
x-intercept:i(2,i0)
yi=i–4(0)i+i8
yi=i8
y-intercept:i(0,i8)
1-2 Copyrighti©i2023iPearsoniEducation,iInc.
