SOLUTION MANUAL
Finite Mathematics & Its Applications
13th Edition by Larry J. Goldstein,
Chapters 1 - 12, Complete
, Contents
Chapter 1: Linear Equations and Straight Lines 1–1
Chapter 2: Matrices 2–1
Chapter 3: Linear Programming, A Geometric Approach 3–1
Chapter 4: The Simplex Method 4–1
Chapter 5: Sets and Counting 5–1
Chapter 6: Probability 6–1
Chapter 7: Probability and Statistics 7–1
Chapter 8: Markov Processes 8–1
Chapter 9: The Theory of Games 9–1
Chapter 10: The Mathematics of Finance 10–1
Chapter 11: Logic 11–1
Chapter 12: Difference Equations and Mathematical Models 12–1
, Chapter 1
Exercises 1.1 5
6. Left 1, down
2
1. Right 2, up 3 y
y
(2, 3)
x
x
( )
–1, – 52
7. Left 20, up 40
2. Left 1, up 4 y
y
(–20, 40)
(–1, 4)
x
x
8. Right 25, up 30
3. Down 2 y
y
(25, 30)
x
x
(0, –2)
9. Point Q is 2 units to the left and 2 units up or
4. Right 2
y (—2, 2).
10. Point P is 3 units to the right and 2 units down or
(3,—2).
x
(2, 0) 1
11. —2(1) + (3) = —2 +1 = —1so yes the point is
3
on the line.
5. Left 2, up 1 1
y 12. —2(2) + (6) = —1 is false, so no the point is not
3
on the line
(–2, 1)
x
Copyright © 2023 Pearson Education, Inc. 1-1
, Chapter 1: Linear Equations and Straight Lines ISM: Finite Math
1 24. 0 = 5
13 —2x + y = —1 Substitute the x and y no solution
3
. x-intercept: none
coordinates of the point into the equation:
f 1 hı f h When x = 0, y = 5
' , 3 → —2 ' 1 ı + 1 (3) = —1 → —1+1 = —1 is y-intercept: (0, 5)
y' ı 'y ıJ
2 J 2 3
a false statement. dSo dno dthe dpoint dis dnot 25. dWhen dy d= d0, dx
don dthedline. d= d7 dx-intercept:
d(7, d0)d0 d= d7
f 1h f1 h
14 —2 ' ı + ' ı (—1) d=d—1 d is dtrue dso dyes dthe no dsolution
.
dpoint dis
'y3 ıJ d d d'y3 ıJ y-intercept: dnone
on dthe dline. 26. d 0 d= d–8x
15. d m d= d5, db x d= d0
d= d8
x-intercept: d(0, d0)
y d= d–8(0)
16. d m d= d–2 dand db d= d– y d= d0
6 y-intercept: d(0, d0)
17. d y d= d0x d+ d3; dm d=
d0, db d= d3
2d 2d 1d
y d= d x d+d0; d m d= d , 27 0 d= d x d – d1
18 3
. .
d b d= d0 x d= d3
3 3
19. d 14x d+d7 dy d= x-intercept: d(3, d0)
1d
d21 y d = d (0) d– d1
3
7 dy d = d—14x d+
y d= d–1
d21
y d = d—2x d+d3
y-intercept: d(0, d–1)
20 x d— dy d = d3 y
. —y d = d—x d+d3
y d = dx d—d3
(3, 0)
21. d d d 3x d= x
d5 (0, –1)
5
x d= d
3
28. When dx d= d0, dy d= d0.
1 2
22 – x d+ y d = d10
. 2 3 d+15
2d 1d 4
y d= d x
d+10
3 2
3d
y d= d x
1-2 Copyright © 2023 Pearson Education, Inc.
Finite Mathematics & Its Applications
13th Edition by Larry J. Goldstein,
Chapters 1 - 12, Complete
, Contents
Chapter 1: Linear Equations and Straight Lines 1–1
Chapter 2: Matrices 2–1
Chapter 3: Linear Programming, A Geometric Approach 3–1
Chapter 4: The Simplex Method 4–1
Chapter 5: Sets and Counting 5–1
Chapter 6: Probability 6–1
Chapter 7: Probability and Statistics 7–1
Chapter 8: Markov Processes 8–1
Chapter 9: The Theory of Games 9–1
Chapter 10: The Mathematics of Finance 10–1
Chapter 11: Logic 11–1
Chapter 12: Difference Equations and Mathematical Models 12–1
, Chapter 1
Exercises 1.1 5
6. Left 1, down
2
1. Right 2, up 3 y
y
(2, 3)
x
x
( )
–1, – 52
7. Left 20, up 40
2. Left 1, up 4 y
y
(–20, 40)
(–1, 4)
x
x
8. Right 25, up 30
3. Down 2 y
y
(25, 30)
x
x
(0, –2)
9. Point Q is 2 units to the left and 2 units up or
4. Right 2
y (—2, 2).
10. Point P is 3 units to the right and 2 units down or
(3,—2).
x
(2, 0) 1
11. —2(1) + (3) = —2 +1 = —1so yes the point is
3
on the line.
5. Left 2, up 1 1
y 12. —2(2) + (6) = —1 is false, so no the point is not
3
on the line
(–2, 1)
x
Copyright © 2023 Pearson Education, Inc. 1-1
, Chapter 1: Linear Equations and Straight Lines ISM: Finite Math
1 24. 0 = 5
13 —2x + y = —1 Substitute the x and y no solution
3
. x-intercept: none
coordinates of the point into the equation:
f 1 hı f h When x = 0, y = 5
' , 3 → —2 ' 1 ı + 1 (3) = —1 → —1+1 = —1 is y-intercept: (0, 5)
y' ı 'y ıJ
2 J 2 3
a false statement. dSo dno dthe dpoint dis dnot 25. dWhen dy d= d0, dx
don dthedline. d= d7 dx-intercept:
d(7, d0)d0 d= d7
f 1h f1 h
14 —2 ' ı + ' ı (—1) d=d—1 d is dtrue dso dyes dthe no dsolution
.
dpoint dis
'y3 ıJ d d d'y3 ıJ y-intercept: dnone
on dthe dline. 26. d 0 d= d–8x
15. d m d= d5, db x d= d0
d= d8
x-intercept: d(0, d0)
y d= d–8(0)
16. d m d= d–2 dand db d= d– y d= d0
6 y-intercept: d(0, d0)
17. d y d= d0x d+ d3; dm d=
d0, db d= d3
2d 2d 1d
y d= d x d+d0; d m d= d , 27 0 d= d x d – d1
18 3
. .
d b d= d0 x d= d3
3 3
19. d 14x d+d7 dy d= x-intercept: d(3, d0)
1d
d21 y d = d (0) d– d1
3
7 dy d = d—14x d+
y d= d–1
d21
y d = d—2x d+d3
y-intercept: d(0, d–1)
20 x d— dy d = d3 y
. —y d = d—x d+d3
y d = dx d—d3
(3, 0)
21. d d d 3x d= x
d5 (0, –1)
5
x d= d
3
28. When dx d= d0, dy d= d0.
1 2
22 – x d+ y d = d10
. 2 3 d+15
2d 1d 4
y d= d x
d+10
3 2
3d
y d= d x
1-2 Copyright © 2023 Pearson Education, Inc.
