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Section 2.1: # 19, 35, 47, 65Section 2.2: # 41, 45, 47, 55, 65Section 2.3: # 3,9, 17, 23, 35,Those applications and those questions which are circled.

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In Problems 15–42, solve each system of equations. If the system has no solution, say that it is inconsistent.

y = 13

5x + 3y = 5

3x – 5y = 2

15.

16.

17.

2x + 3y = 12

2x – 3y = -8

5x + 4y = 1

5x

2x + 4y

=

18.

3x – 5y = -10

19.

2x + y = 1

4x + 2y = 3

20.

x – y = 5

– 3x + 3y = 2

21

x + 2y = 4

2x + 4y = 8

22.

| 3x – y = 7

9x – 3y = 21

2x + 3y = 6

x

+

2x – 3y = -1

10x + y = 11

23.

J3х – 2y = 0

5x + 10y = 4

y = -2

24

25.

1

26.

2

y

11

X-

– 2y =

8

1 1

x + y =

3

–

39

27.

28.

1 3

X

= -5

zy

3

3

x+

4

ЗУ

29.

y = 6

2x – 3z = 16

2y + z = 4

30.

2x +

y =

-4

-2y + 4z = 0

3x – 2z = -11

0

1

-X-

4

y = -1

3y

4

31.

x – 2y + 3z = 7

2x + y + z = 4

– 3x + 2y

2z = -10

32.

2x + y – 3z = -2

-2x + 2y + z = -9

3x – 4y – 3z = 15

33

x – y – 2 = 1

2x + 3y + z = 2

3x + 2y = 0

34.

2x – 3y – z = 0

–x + 2y + z = 5

3x – 4y – z = 1

35.

x – y – 2 = 1

-x + 2y – 32 = -4

3x – 2y – 72 = 0

36.

2x 3y – z=0

3x + 2y + 2z = 2

x + 5y + 3z = 2

37.

2x 2y + 3z = 6

4x – 3y + 2z = 0

– 2x + 3y – 72 = 1

38.

3x 2y + 2z = 6

7x – 3y + 2z = -1

2x – 3y + 4z = 0

0

39.

x + y – 2 = 6

3x 2y + z = -5

x + 3y – 2z = 14

40.

X- y + z = -4

2x 3y + 4z = -15

5x + y – 2z = 12

–

41.

{

x + 2y – z = -3

2x – 4y + 2 = – 7

-2x + 2y – 3z = 4

42.

x + 4y – 3z = -8

3x y + 3z = 12

x + y + z = 1

4

many who paid were adults? How many were seniors?

47. Mixing Nuts A store sells cashews for $5.00 per pound and

peanuts for $1.50 per pound. The manager decides to mix 30

pounds of peanuts with some cashews and sell the mixture for

$3.00 per pound. How many pounds of cashews should be

mixed with the peanuts so that the mixture will produce the

same revenue as would selling the nuts separately?

65. Financial Planning Nathan wants to invest long term the

$70,000 profit he made on the sale of his house. Over 10 years

he hopes to have earnings averaging $5000 per year. Based on

the yearly average return for 10 years ending December 31,

2009, his financial advisor recommended three funds: Mutual

Shares at 4%, Franklin Strategic Income at 6%, and Franklin

Small Cap Value at 8% that would allow Nathan to achieve his

goal while providing diversification.

(a) Prepare a table showing the various ways Nathan can

achieve his goal.

(b) What advice would you give him regarding the amount to

invest and the choices available?

Source: Franklin Templeton

In Problems 37–54, solve each system of equations using Gaussian elimination or Gauss-Jordan elimination. If the system has no solution,

say it is inconsistent.

$2x – 3y = 6

3x + 9y = 4

2x – 3y = 0

37.

39

16x – 9y = 10

2x + 6y = 1

4x + 9 = 5

4y = 3

2x + 6y = 4

3x + 5y = 5

41.

16x + 2y = 1

5x + 15y = 10

6x + 10y = 10

38.

53x

40.

42.

E

x + y = 1

4x – y

=

43.

44

.

4

5

45

2

3x

2y

2x + y + z = 6

X-Y

z = -3

3x + y + 2z = 7

شما نمايا

II

3x + y = 2

46.

x + y + z = 5

2x – y + z = 2

x + 2y – z = 3

47.

2x – 2y – z = 2

2x + 3y + z = 2

3x + 2y = 0

48.

2x –

y – z= -5

x + y + z = 2

x + 2y + 2z = 5

49.

2x + y –

z = 2

x + 3y + 2z = 1

x + y + z = 2

50.

2x + 2y + z = 6

X- y- Z-2

x – 2y – 2z = -5

51.

x + y

z = 0

4x + 4y

4z = -1

2x + y + z = 2

2

3x +

y-2

=

52.

x + y – 2 = 0

4x + 2y – 4z = 0

x + 2y + 2 = 0

53.

2x –

54.

y + z = 1

8

x – 3y = 1

2x – y + z = 1

8

x + 2y + z =

3

4x + 2y

=

In Problems 55-60, use a graphing utility to find the row echelon form (REF) and the reduced row echelon form (RREF) of the augmented

matrix of each of the following systems. Solve each system. If the system has no solution, say it is inconsistent.

2x – 2y + z = 2

X-Sy + 2z = 1

x + y = -1

x + y + z = 4

55.

2

56.

0

x-y-z=

2x + -y-

z = 0

y – 2 =

y – 2 = -4

1

X- Z=

57.

0

1

1

=

X1

40

58.

2x + y + z = 6

x – y – 2 = -3

3x + y + 2z = 7

59.

x1 + x2 + x3 + x4 = 20

x2 + x3 + x4 = 0

x3 + x4 = 13

X2 – 2×4 = -5

60.

2×2 + 3×3 4×4

4×2 + 6×4 = -10

X3 X4 = 12

X2 + 2×4 = -10

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