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 sQ sis s2 sunits sto sthe sleft sand s2 sunits sup sor
4. Right 2
y (—2, s2).
10. Point sP sis s3 sunits sto sthe sright sand s2 sunits sdown sor
(3,—2).
x
(2, 0) 1s
11. —2(1) s+ s (3) s= s—2 s+1 s= s—1so s yes s the s point s is
3
on sthe
sline.
5. Left s2, sup
s1 12. 1s
y
—2(2) s+ s (6) s= s—1 sis s false, s so s no s the s point s is s not
3
on sthe
sline
(–2, 1)
x
Copyright © 2023 Pearson Education, Inc. 1-1
, Chapter 1: Linear Equations and Straight Lines ISM: Finite Math
1s 24. s 0 s= s5
13 —2x s+ s y s = s—1 s Substitute s the s x s and s y no ssolution
3
. x-intercept:
coordinates sof sthe spoint sinto sthe sequation:
f 1 s ıhs f h snone sWhen sx
' ,s3 → s—2 ' 1 ı + s1 s(3)s=s—1 s→ s—1+1 s=s—1 s is s= s0, sy s= s5sy-
y' ı ' ı
intercept: s(0, s5)
2 s s sJ ys2J 3
a sfalse sstatement. sSo sno sthe spoint sis snot 25. sWhen sy s= s0, sx
son sthesline. s= s7 sx-intercept:
s(7, s0)s0 s= s7
f 1h f1 h
14 —2 ' ı + ' ı (—1) s=s—1 s is strue sso syes sthe spoint no ssolution
.
sis
'y3 ıJ s s s'y3 ıJ y-intercept: snone
on sthe sline. 26. s 0 s= s–8x
15. s m s= s5, sb s= x s= s0
s8
x-intercept: s(0, s0)
y s= s–8(0)
16. s m s= s–2 sand sb s= s–6 y s= s0
y-intercept: s(0, s0)
17. s y s= s0x s+ s3; sm s= s0,
sb s= s3
2s 2s 1s
y s= s x s+s0; s m s= s , s b 27 0 s= s x s– s1
18 3
. .
s= s0 x s= s3
3 3
19. s 14x s+s7 sy s= x-intercept: s(3, s0)
1s
s21 y s = s (0) s– s1
3
7 sy s= s—14x s+s21
y s= s–1
y s = s—2x s+s3
y-intercept: s(0, s–1)
20 x s— sy s = s3 y
. —y s = s—x s+s3
y s = sx s—s3
(3, 0) x
21. s s s 3x s= s5
5 (0, –1)
x s= s
3
1 2
28. When sx s= s0, sy s= s0.
22 – x s+ y s =s10
. 2 3 When sx s= s1, sy s= s2.
2s 1s y
y s= s x
s+10
3 2 (1, 2)
3s x
y s= s x (0, 0)
s+15
4
23. 0 s= s—4x s+s8
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 sQ sis s2 sunits sto sthe sleft sand s2 sunits sup sor
4. Right 2
y (—2, s2).
10. Point sP sis s3 sunits sto sthe sright sand s2 sunits sdown sor
(3,—2).
x
(2, 0) 1s
11. —2(1) s+ s (3) s= s—2 s+1 s= s—1so s yes s the s point s is
3
on sthe
sline.
5. Left s2, sup
s1 12. 1s
y
—2(2) s+ s (6) s= s—1 sis s false, s so s no s the s point s is s not
3
on sthe
sline
(–2, 1)
x
Copyright © 2023 Pearson Education, Inc. 1-1
, Chapter 1: Linear Equations and Straight Lines ISM: Finite Math
1s 24. s 0 s= s5
13 —2x s+ s y s = s—1 s Substitute s the s x s and s y no ssolution
3
. x-intercept:
coordinates sof sthe spoint sinto sthe sequation:
f 1 s ıhs f h snone sWhen sx
' ,s3 → s—2 ' 1 ı + s1 s(3)s=s—1 s→ s—1+1 s=s—1 s is s= s0, sy s= s5sy-
y' ı ' ı
intercept: s(0, s5)
2 s s sJ ys2J 3
a sfalse sstatement. sSo sno sthe spoint sis snot 25. sWhen sy s= s0, sx
son sthesline. s= s7 sx-intercept:
s(7, s0)s0 s= s7
f 1h f1 h
14 —2 ' ı + ' ı (—1) s=s—1 s is strue sso syes sthe spoint no ssolution
.
sis
'y3 ıJ s s s'y3 ıJ y-intercept: snone
on sthe sline. 26. s 0 s= s–8x
15. s m s= s5, sb s= x s= s0
s8
x-intercept: s(0, s0)
y s= s–8(0)
16. s m s= s–2 sand sb s= s–6 y s= s0
y-intercept: s(0, s0)
17. s y s= s0x s+ s3; sm s= s0,
sb s= s3
2s 2s 1s
y s= s x s+s0; s m s= s , s b 27 0 s= s x s– s1
18 3
. .
s= s0 x s= s3
3 3
19. s 14x s+s7 sy s= x-intercept: s(3, s0)
1s
s21 y s = s (0) s– s1
3
7 sy s= s—14x s+s21
y s= s–1
y s = s—2x s+s3
y-intercept: s(0, s–1)
20 x s— sy s = s3 y
. —y s = s—x s+s3
y s = sx s—s3
(3, 0) x
21. s s s 3x s= s5
5 (0, –1)
x s= s
3
1 2
28. When sx s= s0, sy s= s0.
22 – x s+ y s =s10
. 2 3 When sx s= s1, sy s= s2.
2s 1s y
y s= s x
s+10
3 2 (1, 2)
3s x
y s= s x (0, 0)
s+15
4
23. 0 s= s—4x s+s8
1-2 Copyright © 2023 Pearson Education, Inc.
