SOLUTION MANUAL
Finite Mathematics & Its Applications
13th Edition by Ḡoldstein Chapters 1 - 12
, Contents
Chapter 1: Linear Equations and Straiḡht Lines 1–1
Chapter 2: Matrices 2–1
Chapter 3: Linear Proḡramminḡ, A Ḡeometric Approach 3–1
Chapter 4: The Simplex Method 4–1
Chapter 5: Sets and Countinḡ 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 Ḡames 9–1
Chapter 10: The Mathematics of Finance 10–1
Chapter 11: Loḡic 11–1
Chapter 12: Difference Equations and Mathematical Models 12–1
, Chapter 1
Exercises 1.1 5
6. Left 1, down
2
1. Riḡht 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. Riḡht 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. Riḡht 2
y (—2, 2).
10. Point P is 3 units to the riḡht 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: When x = 0, y = 5
f 1 ıh f h
' , 3 → —2 ' 1 ı + 1 (3) = —1 → —1+1 = —1 is y-intercept: (0, 5)
y' ı 'y Jı
2 J 2 3
a false statement. So no the point is not on theline. 25. When y = 0, x = 7x-
f 1 h f1 h intercept: (7, 0) 0
—2 ' ı + ' ı(—1) = —1 is true so yes the point is =7
14. no solution
'y 3ıJ 'y 3ıJ y-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 y = –8(0)
y=0
17. y = 0x + 3; m = 0, b = 3 y-intercept: (0, 0)
2 2 1
18. y = x + 0; m = , b = 0 27. 0 = x – 1
3 3 3
x=3
19. 14x +7 y = 21 x-intercept: (3, 0)
1
7 y = —14x + 21 y = (0) – 1
3
y = —2x + 3 y = –1
y-intercept: (0, –1)
20. x — y = 3 y
—y = —x + 3
y = x —3
(3, 0)
21. 3x = 5 x
5 (0, –1)
x=
3
1 2 28. When x = 0, y = 0.
22. – 2 x + 3 y = 10 When x = 1, y = 2.
2 1 y
y = x +10
3 2
3
y = x +15 (1, 2)
4 x
(0, 0)
23. 0 = —4x + 8
4x = 8
x=2
x-intercept: (2, 0)
y = –4(0) + 8
y=8
y-intercept: (0, 8)
1-2 Copyright © 2023 Pearson Education, Inc.
Finite Mathematics & Its Applications
13th Edition by Ḡoldstein Chapters 1 - 12
, Contents
Chapter 1: Linear Equations and Straiḡht Lines 1–1
Chapter 2: Matrices 2–1
Chapter 3: Linear Proḡramminḡ, A Ḡeometric Approach 3–1
Chapter 4: The Simplex Method 4–1
Chapter 5: Sets and Countinḡ 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 Ḡames 9–1
Chapter 10: The Mathematics of Finance 10–1
Chapter 11: Loḡic 11–1
Chapter 12: Difference Equations and Mathematical Models 12–1
, Chapter 1
Exercises 1.1 5
6. Left 1, down
2
1. Riḡht 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. Riḡht 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. Riḡht 2
y (—2, 2).
10. Point P is 3 units to the riḡht 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: When x = 0, y = 5
f 1 ıh f h
' , 3 → —2 ' 1 ı + 1 (3) = —1 → —1+1 = —1 is y-intercept: (0, 5)
y' ı 'y Jı
2 J 2 3
a false statement. So no the point is not on theline. 25. When y = 0, x = 7x-
f 1 h f1 h intercept: (7, 0) 0
—2 ' ı + ' ı(—1) = —1 is true so yes the point is =7
14. no solution
'y 3ıJ 'y 3ıJ y-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 y = –8(0)
y=0
17. y = 0x + 3; m = 0, b = 3 y-intercept: (0, 0)
2 2 1
18. y = x + 0; m = , b = 0 27. 0 = x – 1
3 3 3
x=3
19. 14x +7 y = 21 x-intercept: (3, 0)
1
7 y = —14x + 21 y = (0) – 1
3
y = —2x + 3 y = –1
y-intercept: (0, –1)
20. x — y = 3 y
—y = —x + 3
y = x —3
(3, 0)
21. 3x = 5 x
5 (0, –1)
x=
3
1 2 28. When x = 0, y = 0.
22. – 2 x + 3 y = 10 When x = 1, y = 2.
2 1 y
y = x +10
3 2
3
y = x +15 (1, 2)
4 x
(0, 0)
23. 0 = —4x + 8
4x = 8
x=2
x-intercept: (2, 0)
y = –4(0) + 8
y=8
y-intercept: (0, 8)
1-2 Copyright © 2023 Pearson Education, Inc.
