SOLUTION MANUAL
Finite Mathematics & Its Applications
13th Edition by Goldstein Chapters 1 - 12
, Contents
Chapter 1: Linear Equations and Straight Lines
m m m m m 1–1
Chapter 2: Matrices
m 2–1
Chapter 3: Linear Programming, A Geometric Approach
m m m m m 3–1
Chapter 4: The Simplex Method
m m m 4–1
Chapter 5: Sets and Counting
m m m 5–1
Chapter 6: Probability
m 6–1
Chapter 7: Probability and Statistics
m m m 7–1
Chapter 8: Markov Processes
m m 8–1
Chapter 9: The Theory of Games
m m m m 9–1
Chapter 10: The Mathematics of Finance
m m m m 10–1
Chapter 11: Logic
m 11–1
Chapter 12: Difference Equations and Mathematical Models
m m m m m 12–1
, Chapter 1 m
Exercisesm1.1 5
6.m Leftm1,mdownm
2
1. Rightm2,mupm3 y
y
(2,m3
) x
x
(–1, m–
2
m
5
)m
7.m Leftm20,mupm40
2. Leftm1,mupm4 y
y
(–20,m40)
(–1,m4)
x
x
8.m Rightm25,mupm30
3.m Downm2 y
y
(25,m30)
x
x
(0,m–2)
9. PointmQmism2munitsmtomthemleftmandm2munitsmupmor
4. Rightm2
y (—2,m2).
10. PointmPmism3munitsmtomthemrightmandm2munitsmdownmor
(3,—2).
x
(2,m0 1m
) 11. —2(1)m+m (3)m=m—2m+1m=m—1som yesm them pointm is
3
onmthemline.
5. Leftm2,mupm1 1m
y 12. —2(2)m+m (6)m=m—1mism false,m som nom them pointm ism not
3
onmthemline
(–2,m1)
x
Copyrightm©m2023mPearsonmEducation,mIn 1-1
c.
, Chapterm1:mLinearmEquationsmandmStraightmLin ISM:mFinitemMat
es h
1m 24.m 0m=m5
13. —2xm+m ym =m—1m Substitutem them xm andm y nomsolution
3 x-
coordinatesmofmthempointmintomthemequation: intercept:mnonemW
f 1m ıhm f h
' ,m3 →m—2 ' 1 ı +m1m(3)m=m—1m→m—1+1m=m—1m is henmxm=m0,mym=m5my
y' ı -intercept:m(0,m5)
J ı
2mmm'm ym2J 3
amfalsemstatement.mSomnomthempointmismnotmonmtheml 25.mWhenmym=m0,mxm=m7
ine. mx-
f 1 h f1h intercept:m(7,m0)m0m
14. —2 ' ı + ' ı(—1)m=m—1m ismtruemsomyesmthempointmis =m7
nomsolution
'y3 ıJmmm'y3 ıJ y-intercept:mnone
onmthemline. 26.m 0m=m–8x
15.m mm=m5,mbm=m8 xm=m0
x-intercept:m(0,m0)
16.m mm=m–2mandmbm=m–6 ym=m–8(0)
ym=m0
17.m ym=m0xm+m3;mmm=m0,mbm= y-intercept:m(0,m0)
m3
2m 2m 1m
18. ym=m xm+m0;m mm=m ,m bm=m0 27. 0m=m xm–m1
3 3 3
xm=m3
19.m 14xm+m7mym=m21 x-intercept:m(3,m0)
1m
7mym=m—14xm+m21 ym =m (0)m–m1
3
ym =m—2xm+m3 ym=m–1
y-intercept:m(0,m–1)
20. xm—mym =m3 y
—ym =m—xm+m3
ym=mxm—m3
(3,m0)
21.mmm 3xm=m5 x
5 (0,m–1)
xm=m
3
1 2 28. Whenmxm=m0,mym=m0.
22. – 2 xm+ 3 ym =m10 Whenmxm=m1,mym=m2.
2m 1m y
ym=m xm+10
3 2
3m
ym =m xm+15 (1,m2)
4 x
(0,m0)
23. 0m=m—4xm+m8
4xm =m8
xm=m2
x-intercept:m(2,m0)
ym=m–4(0)m+m8
ym=m8
y-intercept:m(0,m8)
1-2 Copyrightm©m2023mPearsonmEducation,mIn
c.
