SOLUTION MANUAL s
Finite Mathematics & Its Applications
s s s s
13th Edition by Larry J. Goldstein,
s s s s s
Chapters 1 - 12, Complete
s s s s
, Contents
Chapter 1: Linear Equations and Straight Lines
s s s s s 1–1
Chapter 2: Matrices
s 2–1
Chapter 3: Linear Programming, A Geometric Approach
s s s s s 3–1
Chapter 4: The Simplex Method
s s s 4–1
Chapter 5: Sets and Counting
s s s 5–1
Chapter 6: Probability
s 6–1
Chapter 7: Probability and Statistics
s s s 7–1
Chapter 8: Markov Processes
s s 8–1
Chapter 9: The Theory of Games
s s s s 9–1
Chapter 10: The Mathematics of Finance
s s s s 10–1
Chapter 11: Logic
s 11–1
Chapter 12: Difference Equations and Mathematical Models
s s s s s 12–1
, Chapter 1 s
Exercises s1.1 5
6. s Left s1, sdown s
2
1. Right s2, sup s3 y
y
(2, s3)
x
x
( –1, s – s25
)
s
7. s Left s20, sup s40
2. Left s1, sup s4 y
y
(–20, s40)
(–1, s4)
x
x
8. s Right s25, sup s30
3. s Down s2 y
y
(25, s30)
x
x
(0, s–2)
9. Point sQ sis s2 sunits sto sthe sleft sand s2 sunits sup sor
4. Right s2
y (—2,s2).
10. Point sP sis s3 sunits sto sthe sright sand s2 sunits sdown sor
(3,—2).
x
(2, s0) 1s
11. —2(1) s+ s (3) s=s—2 s+1s= s—1so s yes s the s point s is
3
on sthe sline.
5. Left s2, sup s1 1s
y 12. —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, s1)
x
Copyright s© s2023 sPearson sEducation, 1-1
sInc.
, Chapter s1: sLinear sEquations sand sStraight ISM: sFinite
sLines sMath
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: snone
coordinates sof sthe spoint sinto sthe sequation:
sWhen sx s= s0, sy s=
f 1 s hıs f h
' ,s3 →s—2 ' 1 ı +s1s(3)s=s—1s→s—1+1s=s—1 s is s5sy-intercept: s(0,
y' ı '
s5)
ı
s 2 s s sJ ys2J 3
a sfalse sstatement. sSo sno sthe spoint sis snot son 25. sWhen sy s= s0, sx s=
sthesline. 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 sis no ssolution
.
'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= s8 x s= s0
x-intercept: s(0, s0)
16. s m s= s–2 sand sb s= s–6 y s= s–8(0)
y s= s0
17. s y s= s0x s+ s3; sm s= s0, sb s= y-intercept: s(0, s0)
s3
2s 2s 1s
y s= s xs+s0; s m s= s , s b s= s0 27 0 s= s x s–s1
18 3
3 3 .
. x s= s3
19. s 14xs+s7sy s=s21 x-intercept: s(3, s0)
1s
7sy s=s—14x s+s21 y s = s (0) s–s1
3
y s =s—2x s+s3
y s= s–1
y-intercept: s(0, s–1)
20 xs— sy s =s3 y
. —y s =s—x s+s3
y s = sxs—s3
(3, s0)
21. s s s 3x s=s5 x
5 (0, s–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
3s
y s = s x s+15 (1, s2)
4 x
(0, s0)
23. 0 s=s—4x s+s8
4x s = s8
x s= s2
x-intercept: s(2, s0)
y s= s–4(0) s+ s8
y s= s8
1-2 Copyright s© s2023 sPearson sEducation,
sInc.
Finite Mathematics & Its Applications
s s s s
13th Edition by Larry J. Goldstein,
s s s s s
Chapters 1 - 12, Complete
s s s s
, Contents
Chapter 1: Linear Equations and Straight Lines
s s s s s 1–1
Chapter 2: Matrices
s 2–1
Chapter 3: Linear Programming, A Geometric Approach
s s s s s 3–1
Chapter 4: The Simplex Method
s s s 4–1
Chapter 5: Sets and Counting
s s s 5–1
Chapter 6: Probability
s 6–1
Chapter 7: Probability and Statistics
s s s 7–1
Chapter 8: Markov Processes
s s 8–1
Chapter 9: The Theory of Games
s s s s 9–1
Chapter 10: The Mathematics of Finance
s s s s 10–1
Chapter 11: Logic
s 11–1
Chapter 12: Difference Equations and Mathematical Models
s s s s s 12–1
, Chapter 1 s
Exercises s1.1 5
6. s Left s1, sdown s
2
1. Right s2, sup s3 y
y
(2, s3)
x
x
( –1, s – s25
)
s
7. s Left s20, sup s40
2. Left s1, sup s4 y
y
(–20, s40)
(–1, s4)
x
x
8. s Right s25, sup s30
3. s Down s2 y
y
(25, s30)
x
x
(0, s–2)
9. Point sQ sis s2 sunits sto sthe sleft sand s2 sunits sup sor
4. Right s2
y (—2,s2).
10. Point sP sis s3 sunits sto sthe sright sand s2 sunits sdown sor
(3,—2).
x
(2, s0) 1s
11. —2(1) s+ s (3) s=s—2 s+1s= s—1so s yes s the s point s is
3
on sthe sline.
5. Left s2, sup s1 1s
y 12. —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, s1)
x
Copyright s© s2023 sPearson sEducation, 1-1
sInc.
, Chapter s1: sLinear sEquations sand sStraight ISM: sFinite
sLines sMath
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: snone
coordinates sof sthe spoint sinto sthe sequation:
sWhen sx s= s0, sy s=
f 1 s hıs f h
' ,s3 →s—2 ' 1 ı +s1s(3)s=s—1s→s—1+1s=s—1 s is s5sy-intercept: s(0,
y' ı '
s5)
ı
s 2 s s sJ ys2J 3
a sfalse sstatement. sSo sno sthe spoint sis snot son 25. sWhen sy s= s0, sx s=
sthesline. 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 sis no ssolution
.
'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= s8 x s= s0
x-intercept: s(0, s0)
16. s m s= s–2 sand sb s= s–6 y s= s–8(0)
y s= s0
17. s y s= s0x s+ s3; sm s= s0, sb s= y-intercept: s(0, s0)
s3
2s 2s 1s
y s= s xs+s0; s m s= s , s b s= s0 27 0 s= s x s–s1
18 3
3 3 .
. x s= s3
19. s 14xs+s7sy s=s21 x-intercept: s(3, s0)
1s
7sy s=s—14x s+s21 y s = s (0) s–s1
3
y s =s—2x s+s3
y s= s–1
y-intercept: s(0, s–1)
20 xs— sy s =s3 y
. —y s =s—x s+s3
y s = sxs—s3
(3, s0)
21. s s s 3x s=s5 x
5 (0, s–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
3s
y s = s x s+15 (1, s2)
4 x
(0, s0)
23. 0 s=s—4x s+s8
4x s = s8
x s= s2
x-intercept: s(2, s0)
y s= s–4(0) s+ s8
y s= s8
1-2 Copyright s© s2023 sPearson sEducation,
sInc.
