SOLUTION MANUAL
Finite Mathematics & Its Applications
13th Edition bẏ Goldstein Chapters 1 - 12
, 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: Probabilitẏ 6–1
Chapter 7: Probabilitẏ and Statistics 7–1
Chapter 8: Markoṿ Processes 8–1
Chapter 9: The Theorẏ 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 ẏ
ẏ
(2, 3)
x
x
(–1, – 52)
7. Left 20, up 40
2. Left 1, up 4 ẏ
ẏ
(–20, 40)
(–1, 4)
x
x
8. Right 25, up 30
3. Down 2 ẏ
ẏ
(25, 30)
x
x
(0, –2)
9. Point Q is 2 units to the left and 2 units up or
4. Right 2
ẏ (—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 ẏes the point is
3
on the line.
5. Left 2, up 1 1
ẏ 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 + ẏ = —1 Substitute the x and ẏ no solution
3 x-intercept: none
coordinates of the point into the equation: When x = 0, ẏ = 5
f 1 hı f h
' , 3 → —2 ' 1 ı + 1 (3) = —1 → —1+1 = —1 is ẏ-intercept: (0, 5)
ẏ' ı 'ẏ ıJ
2 J 2 3
a false statement. So no the point is not on theline. 25. When ẏ = 0, x = 7x-
f 1h f1h intercept: (7, 0) 0
—2 ' ı + ' ı(—1) = —1 is true so ẏes the point is =7
14. no solution
'ẏ3 ıJ 'ẏ3 ıJ ẏ-intercept: none
on the line. 26. 0 = –8x
15. m = 5, b = 8 x=0
x-intercept: (0, 0)
16. m = –2 and b = –6 ẏ = –8(0)
ẏ=0
17. ẏ = 0x + 3; m = 0, b = 3 ẏ-intercept: (0, 0)
2 2 1
18. ẏ = x + 0; m = , b = 0 27. 0 = x – 1
3 3 3
x=3
19. 14x + 7 ẏ = 21 x-intercept: (3, 0)
1
7 ẏ = —14x + 21 ẏ = (0) – 1
3
ẏ = —2x + 3
ẏ = –1
ẏ-intercept: (0, –1)
20. x — ẏ = 3 ẏ
—ẏ = —x + 3
ẏ = x —3
(3, 0)
21. 3x = 5 x
5 (0, –1)
x=
3
1 2 28. When x = 0, ẏ = 0.
22. – 2 x + 3 ẏ = 10 When x = 1, ẏ = 2.
2 1 ẏ
ẏ = x +10
3 2
3
ẏ = x +15 (1, 2)
4 x
(0, 0)
23. 0 = —4x + 8
4x = 8
x =2
x-intercept: (2, 0)
ẏ = –4(0) + 8
ẏ=8
ẏ-intercept: (0, 8)
1-2 Copyright © 2023 Pearson Education, Inc.
Finite Mathematics & Its Applications
13th Edition bẏ Goldstein Chapters 1 - 12
, 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: Probabilitẏ 6–1
Chapter 7: Probabilitẏ and Statistics 7–1
Chapter 8: Markoṿ Processes 8–1
Chapter 9: The Theorẏ 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 ẏ
ẏ
(2, 3)
x
x
(–1, – 52)
7. Left 20, up 40
2. Left 1, up 4 ẏ
ẏ
(–20, 40)
(–1, 4)
x
x
8. Right 25, up 30
3. Down 2 ẏ
ẏ
(25, 30)
x
x
(0, –2)
9. Point Q is 2 units to the left and 2 units up or
4. Right 2
ẏ (—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 ẏes the point is
3
on the line.
5. Left 2, up 1 1
ẏ 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 + ẏ = —1 Substitute the x and ẏ no solution
3 x-intercept: none
coordinates of the point into the equation: When x = 0, ẏ = 5
f 1 hı f h
' , 3 → —2 ' 1 ı + 1 (3) = —1 → —1+1 = —1 is ẏ-intercept: (0, 5)
ẏ' ı 'ẏ ıJ
2 J 2 3
a false statement. So no the point is not on theline. 25. When ẏ = 0, x = 7x-
f 1h f1h intercept: (7, 0) 0
—2 ' ı + ' ı(—1) = —1 is true so ẏes the point is =7
14. no solution
'ẏ3 ıJ 'ẏ3 ıJ ẏ-intercept: none
on the line. 26. 0 = –8x
15. m = 5, b = 8 x=0
x-intercept: (0, 0)
16. m = –2 and b = –6 ẏ = –8(0)
ẏ=0
17. ẏ = 0x + 3; m = 0, b = 3 ẏ-intercept: (0, 0)
2 2 1
18. ẏ = x + 0; m = , b = 0 27. 0 = x – 1
3 3 3
x=3
19. 14x + 7 ẏ = 21 x-intercept: (3, 0)
1
7 ẏ = —14x + 21 ẏ = (0) – 1
3
ẏ = —2x + 3
ẏ = –1
ẏ-intercept: (0, –1)
20. x — ẏ = 3 ẏ
—ẏ = —x + 3
ẏ = x —3
(3, 0)
21. 3x = 5 x
5 (0, –1)
x=
3
1 2 28. When x = 0, ẏ = 0.
22. – 2 x + 3 ẏ = 10 When x = 1, ẏ = 2.
2 1 ẏ
ẏ = x +10
3 2
3
ẏ = x +15 (1, 2)
4 x
(0, 0)
23. 0 = —4x + 8
4x = 8
x =2
x-intercept: (2, 0)
ẏ = –4(0) + 8
ẏ=8
ẏ-intercept: (0, 8)
1-2 Copyright © 2023 Pearson Education, Inc.
