Contents
SOLUTION MANUAL Chapter 1: Linear Equations and Straight Lines
2 2 2 2 2 1–1
Finite Mathematics & Its Applications Chapter 2: Matrices
2 2–1
Chapter 3: Linear Programming, A Geometric Approach
2 2 2 2 2 3–1
13th Edition by Larry J. Goldstein, Chapter 4: The Simplex Method
2 2 2 4–1
Chapter 5: Sets and Counting 5–1
Chapters 1 - 12, Complete 2 2
Chapter 6: Probability
2
2
6–1
Chapter 7: Probability and Statistics
2 2 2 7–1
Chapter 8: Markov Processes
2 2 8–1
Chapter 9: The Theory of Games
2 2 2 2 9–1
Chapter 10: The Mathematics of Finance
2 2 2 2 10–1
Chapter 11: Logic
2 11–1
Chapter 12: Difference Equations and Mathematical Models
2 2 2 2 2 12–1
, Chapter21:2Linear2Equations2and2Straight2Lines ISM:2Finite2Math
12 24.2 02=25
Chapter 1 2
13 —2x2+2 y2 =2—12 Substitute2 the2 x2 and2 y no2solution
3
. x-
Exercises21.1 5 coordinates2of2the2point2into2the2equation:
6.2 Left21,2down2 f 12 ıh2 f h intercept:2none2
2 ' ,23 →2—2 ' 1 ı +212(3)2=2—12→2—1+12=2—12 is When2x2=20,2y2=252
1. Right22,2up23 y y' ı '2 ı
y
y-intercept:2(0,25)
2222 J y22J 3
a2false2statement.2So2no2the2point2is2not2on2t 25.2When2y2=20,2x2=272
he2line. x-
(2,23)
x f 1h f1 h intercept:2(7,20)202
x
14 —2 ' ı + ' ı (—1)2=2—12 is2true2so2yes2the2point2is =27
(–1, – 52 )
2 2
2
.
no2solution
'y3 ıJ222'y3 ıJ y-intercept:2none
on2the2line. 26.2 02=2–8x
7.2 Left220,2up240 15.2 m2=25,2b2=28 x2=20
2. Left21,2up24 y
y x-intercept:2(0,20)
16.2 m2=2–22and2b2=2–6 y2=2–8(0)
(–20,240) y2=20
(–1,24)
17.2 y2=20x2+23;2m2=20,2b2=23 y-intercept:2(0,20)
x
x 12
22 22 02=2 x2–21
18 y2=2 x2+20;2 m2=2 ,2 b2=20 27
3 3 . 3
. x2=23
19.2 14x2+272y2=221 x-intercept:2(3,20)
8.2 Right225,2up230 12
3.2 Down22 72y2=2—14x2+221 y2 =2 (0)2–21
y
y 3
y2 =2—2x2+23
y2=2–1
y-intercept:2(0,2–1)
(25,230) 20 x2—2y2 =23 y
x . —y2 =2—x2+23
x
(0,2–2) y2 =2x2—23
(3,20)
21.222 3x2=25 x
5 (0,2–1)
x2=2
9. Point2Q2is222units2to2the2left2and222units2up2or 3
4. Right22
y (—2,22).
1 2
28. When2x2=20,2y2=20.
10. Point2P2is232units2to2the2right2and222units2down2or 22 – x2+ y2 =210
. 2 3 When2x2=21,2y2=22.
(3,—2). 22 12 y
y2 =2 x2+10
x
(2,20) 3 2
12 32
11. —2(1)2+2 (3)2=2—22+12=2—1so2 yes2 the2 point2 is y2 =2 x2+15 (1,22)
3 4
on2the2line. (0,20) x
23. 02=2—4x2+28
5. Left22,2up21 12
y 12. —2(2)2+2 (6)2=2—12is2 false,2 so2 no2 the2 point2 is2 not 4x2 =28
3
on2the2line x2=22
x-intercept:2(2,20)
y2=2–4(0)2+28
(–2,21)
x y2=28
y-intercept:2(0,28)
1-2 Copyright2©220232Pearson2Education,2Inc.
Copyright2©220232Pearson2Education,2Inc. 1-1
,ISM:2Finite2Math Chapter21:2Linear2Equations2and2Straight2Lines Chapter21:2Linear2Equations2and2Straight2Lines ISM:2Finite2Math
5 32 x2+202=23 35.2 2x2+23y2 =26 12
29 02=2 36.222 x2–5 2y2=21
2 . x2=23 3y2 =2—2x2+26 2 12
. 2 –52y2=2 +1
no2solution x-intercept:2(3,20)
x- 02+2y2=23 y2=— 2 x2+22 –222 x
3 2
intercept:2none 12 1
5 y2=2 x2–2
y2 =23
When2x2=20, y2=2 a. 4x2+262y2 =212 10 5
y-intercept:2(0,23)
f 5 ıh2 y
62y2 =2—4x2+12 1
y-intercept:2 '0,22 2 a. =21
'y 2 ıJ y2=— 2 2x2– y
x2+22 5
y
(0,23)
3
12
(3,20)
Yes —2 y2 =2—2x2+1
x
(0, 52)
2 2
2 5
b. Yes y2 =210x2—25
x No
32
c. x2 =23—2 y
2 b.
5 32 x2=252y2+22252
33 x2=— 2 y2 =2—x2+23
y2 =2x2—22
2 2 12 2
. y2 =2 x2—2
30.2 The2line2coincides2with2the2y-axis. 2
y y2=— 2
x2+22 5 5
3 No
22
x2=20 y2= – x +22
3 c. 22—5x2+102y2 =20
x Yes —102y2 =2—5x2+22
12 1
d. 62—22x2—2y2 =20 y2 =2 x2—2
2 5
12 12 y2 =262—22x2 =2—2x2+26 No
34.2 2 x2—2 (0)2=2—1
2 3 No
31.2 3x2+24(0)2=224 x2=2—2 d. y2=2.1(x2—22)
22 22
x2=28 x2intercept2(–2,20) e. y2=22– 2 x2=2–2 x2+22 y2 =2.1x2—.2
x-intercept:2(8,20) 12 12 3 3 12 1
(0)—2 y2 =2—1 y2 =2 x2—2
3(0)2+242y2 =224 2 3 Yes
10 5
y2=26 y2=23 Yes
f. x2+2y2 =21
y-intercept:2(0,26) y2intercept2(0,23)
y y2 =2—x2+1 e. 102y2—2x2=2—2
No
(0,26) 102y2 =2 x2—22
12 1
y2 =2 x2—2
(8,20)
x 10 5
Yes
f. 1+.5x2 =2 22+252y
52y2=2.5x2—1
12 1
y2 =2 x2—2
10 5
Yes
1-4 Copyright2©220232Pearson2Education,2Inc.
Copyright2©220232Pearson2Education,2Inc. 1-3
, ISM:2Finite2Math Chapter21:2Linear2Equations2and2Straight2Lines Chapter21:2Linear2Equations2and2Straight2Lines ISM:2Finite2Math
37.2 a. x2+2y2 =23 c. 2004f 12—1960
h 2=244 d.222 20322–220102=222 c. 11802 =2 30x2 +1000
y2 =2—x2+23 y2=2' ı (44)2+270 y2=21.15(22)2+214 1802=230x
'2 ı y2=239.3
m2=2–1,2b2=23 y6 J x2=26
$39,300
L3 y2 =27.332+270 The2balance2will2be2$11802after262years.
y2=277.33 43.2 a. x-intercept:2(–18.5,20)
b. 2x2—2y2 =2—2 45. a.
A2person2born2in220042has2a2life2expectancy2 y-intercept:2(0,2869)
In22010,26.1%2of2entering2college2fr
—y2 =2—2x2—22 of277.32years. eshmen2intended2to2major2in2biology.
y2 =22x2+22
m2=22,2b2=22 'f 1 ıh
41.22 a. x-intercept:2 '16122 ,20ı b. 20192—220102=29
L1 y 9 J 1
y2=2 26(9)2+26.1
y-intercept:2(0,25.8)
c. y2=27.6
x2=23y2+2323 7.6%2of2college2freshmen2in220192intende
y2 =2 x2—3 d2to2major2in2biology.
12
y2 =2 x2—1 c.
1
6.82=2 2x2+26.1
3 b.2In220142the2car2insurance2rate2for2a2small2car2 6
12
m2=2 , b2=2–1 was2$869. 0.72=2162x2
3 x2=24.2
c. 20172–220142=23 20102+242=22014
L2
y2=247(3)2+2869 In22014,2the2percent2of2college2freshmen
b.2 In22004,25.82trillion2cigarettes2were2sold. y2=21010 who2intended2to2major2in2biology2was26.8%.
38.2 a. No;252+242≠23
$1010
c. 5.52=2–.036x2+25.8 46. a.
b.222 No;222≠212–21
x2=28.33 d. 14802=247x2+2869 In22010,246.4%2of2college2freshme
c. Yes;22(2)2=212+232and22(4)2=252+23 20042+282=22012 6112=247x n2considered2themselves2middle-of-the-
x2=213 road2politically.
y2=230x2+272 d.222 20282–220042=224
39 20142+132=22027
y2=2–.036(24)2+25.8
. b. 20162—220102=26
a. When2x2=20,2y2=272.2This2is2the2temperatur y2=24.936 The2yearly2rate2will2be2$14802in22027.
4.92trillion y2=246.42—20.31(6)
e2of2the2water2at2time2=202before2the2kettle
y2=244.54
2is2turned2on.
f2 100 ,2 0hı
42.2 a. x-intercept:2(–12.17,20) 44.22 a. x-intercept:2 ''— 44.5%2of2college2freshmen2considered2themselv
y-intercept:2(0,214) y 3 ıJ es2middle-of-the-road2politically2in
b. y2 =230(3)2+272
y-intercept:2(0,21000) 2016.
y2=2162∘2F
c. 43.92=246.42—20.31x
c. Water2boils2when2y2=22122so2we2have
—2.52=2—0.31x
2122=230x2+272.2Solving2for2x2gives
x2=24 32 minutes2or242minutes2402seconds.
2
x2≈28
20102+282=22018
40.2 a. In22018,2the2percent2of2college2freshmen2that
b. In220102the2income2from2ecotourism2was
considered2themselves2middle-of-the-
A2person2born2in219602has2a2life2expecta $14,000.
road2was243.9%.
ncy2of2702years.
f 1 h2 c. 202=21.15x2+214
b. 752=2' ı x2+270 47.2 a. 2018—220122=26
'2 ı x2≈25.22 b. y2 =230(2)2+1000 y2=2433(6)2+221,2593
y6 J y2 =2602+1000
f 1 ıh2 20102+25.222=22015.22 y2 =224,191
52=2' x The2year220152should2have2had2$20,0002i y2 =21060 $24,1912was2the2approximate2average2tuitio
'y6 Jı n2ecotourism2income. $10602will2be2in2the2account2after222years n2in22018.
x2=230 .
19602+2302=21990
1-6 Copyright2©220232Pearson2Education,2Inc.
Copyright2©220232Pearson2Education,2Inc. 1-5
SOLUTION MANUAL Chapter 1: Linear Equations and Straight Lines
2 2 2 2 2 1–1
Finite Mathematics & Its Applications Chapter 2: Matrices
2 2–1
Chapter 3: Linear Programming, A Geometric Approach
2 2 2 2 2 3–1
13th Edition by Larry J. Goldstein, Chapter 4: The Simplex Method
2 2 2 4–1
Chapter 5: Sets and Counting 5–1
Chapters 1 - 12, Complete 2 2
Chapter 6: Probability
2
2
6–1
Chapter 7: Probability and Statistics
2 2 2 7–1
Chapter 8: Markov Processes
2 2 8–1
Chapter 9: The Theory of Games
2 2 2 2 9–1
Chapter 10: The Mathematics of Finance
2 2 2 2 10–1
Chapter 11: Logic
2 11–1
Chapter 12: Difference Equations and Mathematical Models
2 2 2 2 2 12–1
, Chapter21:2Linear2Equations2and2Straight2Lines ISM:2Finite2Math
12 24.2 02=25
Chapter 1 2
13 —2x2+2 y2 =2—12 Substitute2 the2 x2 and2 y no2solution
3
. x-
Exercises21.1 5 coordinates2of2the2point2into2the2equation:
6.2 Left21,2down2 f 12 ıh2 f h intercept:2none2
2 ' ,23 →2—2 ' 1 ı +212(3)2=2—12→2—1+12=2—12 is When2x2=20,2y2=252
1. Right22,2up23 y y' ı '2 ı
y
y-intercept:2(0,25)
2222 J y22J 3
a2false2statement.2So2no2the2point2is2not2on2t 25.2When2y2=20,2x2=272
he2line. x-
(2,23)
x f 1h f1 h intercept:2(7,20)202
x
14 —2 ' ı + ' ı (—1)2=2—12 is2true2so2yes2the2point2is =27
(–1, – 52 )
2 2
2
.
no2solution
'y3 ıJ222'y3 ıJ y-intercept:2none
on2the2line. 26.2 02=2–8x
7.2 Left220,2up240 15.2 m2=25,2b2=28 x2=20
2. Left21,2up24 y
y x-intercept:2(0,20)
16.2 m2=2–22and2b2=2–6 y2=2–8(0)
(–20,240) y2=20
(–1,24)
17.2 y2=20x2+23;2m2=20,2b2=23 y-intercept:2(0,20)
x
x 12
22 22 02=2 x2–21
18 y2=2 x2+20;2 m2=2 ,2 b2=20 27
3 3 . 3
. x2=23
19.2 14x2+272y2=221 x-intercept:2(3,20)
8.2 Right225,2up230 12
3.2 Down22 72y2=2—14x2+221 y2 =2 (0)2–21
y
y 3
y2 =2—2x2+23
y2=2–1
y-intercept:2(0,2–1)
(25,230) 20 x2—2y2 =23 y
x . —y2 =2—x2+23
x
(0,2–2) y2 =2x2—23
(3,20)
21.222 3x2=25 x
5 (0,2–1)
x2=2
9. Point2Q2is222units2to2the2left2and222units2up2or 3
4. Right22
y (—2,22).
1 2
28. When2x2=20,2y2=20.
10. Point2P2is232units2to2the2right2and222units2down2or 22 – x2+ y2 =210
. 2 3 When2x2=21,2y2=22.
(3,—2). 22 12 y
y2 =2 x2+10
x
(2,20) 3 2
12 32
11. —2(1)2+2 (3)2=2—22+12=2—1so2 yes2 the2 point2 is y2 =2 x2+15 (1,22)
3 4
on2the2line. (0,20) x
23. 02=2—4x2+28
5. Left22,2up21 12
y 12. —2(2)2+2 (6)2=2—12is2 false,2 so2 no2 the2 point2 is2 not 4x2 =28
3
on2the2line x2=22
x-intercept:2(2,20)
y2=2–4(0)2+28
(–2,21)
x y2=28
y-intercept:2(0,28)
1-2 Copyright2©220232Pearson2Education,2Inc.
Copyright2©220232Pearson2Education,2Inc. 1-1
,ISM:2Finite2Math Chapter21:2Linear2Equations2and2Straight2Lines Chapter21:2Linear2Equations2and2Straight2Lines ISM:2Finite2Math
5 32 x2+202=23 35.2 2x2+23y2 =26 12
29 02=2 36.222 x2–5 2y2=21
2 . x2=23 3y2 =2—2x2+26 2 12
. 2 –52y2=2 +1
no2solution x-intercept:2(3,20)
x- 02+2y2=23 y2=— 2 x2+22 –222 x
3 2
intercept:2none 12 1
5 y2=2 x2–2
y2 =23
When2x2=20, y2=2 a. 4x2+262y2 =212 10 5
y-intercept:2(0,23)
f 5 ıh2 y
62y2 =2—4x2+12 1
y-intercept:2 '0,22 2 a. =21
'y 2 ıJ y2=— 2 2x2– y
x2+22 5
y
(0,23)
3
12
(3,20)
Yes —2 y2 =2—2x2+1
x
(0, 52)
2 2
2 5
b. Yes y2 =210x2—25
x No
32
c. x2 =23—2 y
2 b.
5 32 x2=252y2+22252
33 x2=— 2 y2 =2—x2+23
y2 =2x2—22
2 2 12 2
. y2 =2 x2—2
30.2 The2line2coincides2with2the2y-axis. 2
y y2=— 2
x2+22 5 5
3 No
22
x2=20 y2= – x +22
3 c. 22—5x2+102y2 =20
x Yes —102y2 =2—5x2+22
12 1
d. 62—22x2—2y2 =20 y2 =2 x2—2
2 5
12 12 y2 =262—22x2 =2—2x2+26 No
34.2 2 x2—2 (0)2=2—1
2 3 No
31.2 3x2+24(0)2=224 x2=2—2 d. y2=2.1(x2—22)
22 22
x2=28 x2intercept2(–2,20) e. y2=22– 2 x2=2–2 x2+22 y2 =2.1x2—.2
x-intercept:2(8,20) 12 12 3 3 12 1
(0)—2 y2 =2—1 y2 =2 x2—2
3(0)2+242y2 =224 2 3 Yes
10 5
y2=26 y2=23 Yes
f. x2+2y2 =21
y-intercept:2(0,26) y2intercept2(0,23)
y y2 =2—x2+1 e. 102y2—2x2=2—2
No
(0,26) 102y2 =2 x2—22
12 1
y2 =2 x2—2
(8,20)
x 10 5
Yes
f. 1+.5x2 =2 22+252y
52y2=2.5x2—1
12 1
y2 =2 x2—2
10 5
Yes
1-4 Copyright2©220232Pearson2Education,2Inc.
Copyright2©220232Pearson2Education,2Inc. 1-3
, ISM:2Finite2Math Chapter21:2Linear2Equations2and2Straight2Lines Chapter21:2Linear2Equations2and2Straight2Lines ISM:2Finite2Math
37.2 a. x2+2y2 =23 c. 2004f 12—1960
h 2=244 d.222 20322–220102=222 c. 11802 =2 30x2 +1000
y2 =2—x2+23 y2=2' ı (44)2+270 y2=21.15(22)2+214 1802=230x
'2 ı y2=239.3
m2=2–1,2b2=23 y6 J x2=26
$39,300
L3 y2 =27.332+270 The2balance2will2be2$11802after262years.
y2=277.33 43.2 a. x-intercept:2(–18.5,20)
b. 2x2—2y2 =2—2 45. a.
A2person2born2in220042has2a2life2expectancy2 y-intercept:2(0,2869)
In22010,26.1%2of2entering2college2fr
—y2 =2—2x2—22 of277.32years. eshmen2intended2to2major2in2biology.
y2 =22x2+22
m2=22,2b2=22 'f 1 ıh
41.22 a. x-intercept:2 '16122 ,20ı b. 20192—220102=29
L1 y 9 J 1
y2=2 26(9)2+26.1
y-intercept:2(0,25.8)
c. y2=27.6
x2=23y2+2323 7.6%2of2college2freshmen2in220192intende
y2 =2 x2—3 d2to2major2in2biology.
12
y2 =2 x2—1 c.
1
6.82=2 2x2+26.1
3 b.2In220142the2car2insurance2rate2for2a2small2car2 6
12
m2=2 , b2=2–1 was2$869. 0.72=2162x2
3 x2=24.2
c. 20172–220142=23 20102+242=22014
L2
y2=247(3)2+2869 In22014,2the2percent2of2college2freshmen
b.2 In22004,25.82trillion2cigarettes2were2sold. y2=21010 who2intended2to2major2in2biology2was26.8%.
38.2 a. No;252+242≠23
$1010
c. 5.52=2–.036x2+25.8 46. a.
b.222 No;222≠212–21
x2=28.33 d. 14802=247x2+2869 In22010,246.4%2of2college2freshme
c. Yes;22(2)2=212+232and22(4)2=252+23 20042+282=22012 6112=247x n2considered2themselves2middle-of-the-
x2=213 road2politically.
y2=230x2+272 d.222 20282–220042=224
39 20142+132=22027
y2=2–.036(24)2+25.8
. b. 20162—220102=26
a. When2x2=20,2y2=272.2This2is2the2temperatur y2=24.936 The2yearly2rate2will2be2$14802in22027.
4.92trillion y2=246.42—20.31(6)
e2of2the2water2at2time2=202before2the2kettle
y2=244.54
2is2turned2on.
f2 100 ,2 0hı
42.2 a. x-intercept:2(–12.17,20) 44.22 a. x-intercept:2 ''— 44.5%2of2college2freshmen2considered2themselv
y-intercept:2(0,214) y 3 ıJ es2middle-of-the-road2politically2in
b. y2 =230(3)2+272
y-intercept:2(0,21000) 2016.
y2=2162∘2F
c. 43.92=246.42—20.31x
c. Water2boils2when2y2=22122so2we2have
—2.52=2—0.31x
2122=230x2+272.2Solving2for2x2gives
x2=24 32 minutes2or242minutes2402seconds.
2
x2≈28
20102+282=22018
40.2 a. In22018,2the2percent2of2college2freshmen2that
b. In220102the2income2from2ecotourism2was
considered2themselves2middle-of-the-
A2person2born2in219602has2a2life2expecta $14,000.
road2was243.9%.
ncy2of2702years.
f 1 h2 c. 202=21.15x2+214
b. 752=2' ı x2+270 47.2 a. 2018—220122=26
'2 ı x2≈25.22 b. y2 =230(2)2+1000 y2=2433(6)2+221,2593
y6 J y2 =2602+1000
f 1 ıh2 20102+25.222=22015.22 y2 =224,191
52=2' x The2year220152should2have2had2$20,0002i y2 =21060 $24,1912was2the2approximate2average2tuitio
'y6 Jı n2ecotourism2income. $10602will2be2in2the2account2after222years n2in22018.
x2=230 .
19602+2302=21990
1-6 Copyright2©220232Pearson2Education,2Inc.
Copyright2©220232Pearson2Education,2Inc. 1-5
