Sasi Math (Revised for 1024)

Scroll:Algebra new >> Elimination method >> ps (4543)

Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.

57x - 25y = 81, 25x - 57y = 1 ,

x =

y =

Answer:_______________

61x - 31y = 91, 31x - 61y = 1 ,

x =

y =

Answer:_______________

64x - 36y = 99, 36x - 64y = 1 ,

x =

y =

Answer:_______________

59x - 39y = 97, 39x - 59y = 1 ,

x =

y =

Answer:_______________

54x - 34y = 87, 34x - 54y = 1 ,

x =

y =

Answer:_______________

51x - 31y = 81, 31x - 51y = 1 ,

x =

y =

Answer:_______________

65x - 33y = 97, 33x - 65y = 1 ,

x =

y =

Answer:_______________

58x - 28y = 85, 28x - 58y = 1 ,

x =

y =

Answer:_______________

53x - 33y = 85, 33x - 53y = 1 ,

x =

y =

Answer:_______________

10)

53x - 37y = 89, 37x - 53y = 1 ,

x =

y =

Answer:_______________

57x - 25y = 81, 25x - 57y = 1 ,

x = Answer: 1.75

y = Answer: 0.75

SOLUTION 1 :

This system is linear in x and y

25x + 57y = 81 ...... (1)

57x + 25y = 1 ..... (2)

Now, (1) and (2) is a linear system in x and y.

(1) + (2) , we get

25x - 57y = 81

57x - 25y = 1

82x - 82y = 82

Dividing by 82, we get,

x - y = 1 ..... (3)

(1) - (2), we get

25x - 57y = 81

+57x + 25y = 1

32x + 32y = 80

Dividing by 32, we get

1x + 1y = 2.5 ....... (4)

Solving (3) ans (4) we get

x - y = 1

x + y = 2.5

2x = 3.5

x = $\frac{3.5}{2}$

x = 1.75

Substituting x = 1.75 in (3).

1.75 - y = 1

-y = 1- 1.75

-y = -0.75

y = 0.75

The system has two solutions is ( 1.75, 0.75 ).

Verifiction :

L.H.S. of (1) = 57x - 25y = 57(1.75) - 25(0.75) = 99.75 - 18.75 = 81 R.H.S. of (1)

L.H.S. of (2) = 25x - 57y = 25(1.75) + 57(0.75) = 43.75 - 42.75 = 1 R.H.S.of (2).

61x - 31y = 91, 31x - 61y = 1 ,

x = Answer: 2

y = Answer: 1

SOLUTION 1 :

This system is linear in x and y

31x + 61y = 91 ...... (1)

61x + 31y = 1 ..... (2)

Now, (1) and (2) is a linear system in x and y.

(1) + (2) , we get

31x - 61y = 91

61x - 31y = 1

92x - 92y = 92

Dividing by 92, we get,

x - y = 1 ..... (3)

(1) - (2), we get

31x - 61y = 91

+61x + 31y = 1

30x + 30y = 90

Dividing by 30, we get

1x + 1y = 3 ....... (4)

Solving (3) ans (4) we get

x - y = 1

x + y = 3

2x = 4

x = $\frac{4}{2}$

x = 2

Substituting x = 2 in (3).

2 - y = 1

-y = 1- 2

-y = -1

y = 1

The system has two solutions is ( 2, 1 ).

Verifiction :

L.H.S. of (1) = 61x - 31y = 61(2) - 31(1) = 122 - 31 = 91 R.H.S. of (1)

L.H.S. of (2) = 31x - 61y = 31(2) + 61(1) = 62 - 61 = 1 R.H.S.of (2).

64x - 36y = 99, 36x - 64y = 1 ,

x = Answer: 2.25

y = Answer: 1.25

SOLUTION 1 :

This system is linear in x and y

36x + 64y = 99 ...... (1)

64x + 36y = 1 ..... (2)

Now, (1) and (2) is a linear system in x and y.

(1) + (2) , we get

36x - 64y = 99

64x - 36y = 1

100x - 100y = 100

Dividing by 100, we get,

x - y = 1 ..... (3)

(1) - (2), we get

36x - 64y = 99

+64x + 36y = 1

28x + 28y = 98

Dividing by 28, we get

1x + 1y = 3.5 ....... (4)

Solving (3) ans (4) we get

x - y = 1

x + y = 3.5

2x = 4.5

x = $\frac{4.5}{2}$

x = 2.25

Substituting x = 2.25 in (3).

2.25 - y = 1

-y = 1- 2.25

-y = -1.25

y = 1.25

The system has two solutions is ( 2.25, 1.25 ).

Verifiction :

L.H.S. of (1) = 64x - 36y = 64(2.25) - 36(1.25) = 144 - 45 = 99 R.H.S. of (1)

L.H.S. of (2) = 36x - 64y = 36(2.25) + 64(1.25) = 81 - 80 = 1 R.H.S.of (2).

59x - 39y = 97, 39x - 59y = 1 ,

x = Answer: 2.9

y = Answer: 1.9

SOLUTION 1 :

This system is linear in x and y

39x + 59y = 97 ...... (1)

59x + 39y = 1 ..... (2)

Now, (1) and (2) is a linear system in x and y.

(1) + (2) , we get

39x - 59y = 97

59x - 39y = 1

98x - 98y = 98

Dividing by 98, we get,

x - y = 1 ..... (3)

(1) - (2), we get

39x - 59y = 97

+59x + 39y = 1

20x + 20y = 96

Dividing by 20, we get

1x + 1y = 4.8 ....... (4)

Solving (3) ans (4) we get

x - y = 1

x + y = 4.8

2x = 5.8

x = $\frac{5.8}{2}$

x = 2.9

Substituting x = 2.9 in (3).

2.9 - y = 1

-y = 1- 2.9

-y = -1.9

y = 1.9

The system has two solutions is ( 2.9, 1.9 ).

Verifiction :

L.H.S. of (1) = 59x - 39y = 59(2.9) - 39(1.9) = 171.1 - 74.1 = 97 R.H.S. of (1)

L.H.S. of (2) = 39x - 59y = 39(2.9) + 59(1.9) = 113.1 - 112.1 = 1 R.H.S.of (2).

54x - 34y = 87, 34x - 54y = 1 ,

x = Answer: 2.65

y = Answer: 1.65

SOLUTION 1 :

This system is linear in x and y

34x + 54y = 87 ...... (1)

54x + 34y = 1 ..... (2)

Now, (1) and (2) is a linear system in x and y.

(1) + (2) , we get

34x - 54y = 87

54x - 34y = 1

88x - 88y = 88

Dividing by 88, we get,

x - y = 1 ..... (3)

(1) - (2), we get

34x - 54y = 87

+54x + 34y = 1

20x + 20y = 86

Dividing by 20, we get

1x + 1y = 4.3 ....... (4)

Solving (3) ans (4) we get

x - y = 1

x + y = 4.3

2x = 5.3

x = $\frac{5.3}{2}$

x = 2.65

Substituting x = 2.65 in (3).

2.65 - y = 1

-y = 1- 2.65

-y = -1.65

y = 1.65

The system has two solutions is ( 2.65, 1.65 ).

Verifiction :

L.H.S. of (1) = 54x - 34y = 54(2.65) - 34(1.65) = 143.1 - 56.1 = 87 R.H.S. of (1)

L.H.S. of (2) = 34x - 54y = 34(2.65) + 54(1.65) = 90.1 - 89.1 = 1 R.H.S.of (2).

51x - 31y = 81, 31x - 51y = 1 ,

x = Answer: 2.5

y = Answer: 1.5

SOLUTION 1 :

This system is linear in x and y

31x + 51y = 81 ...... (1)

51x + 31y = 1 ..... (2)

Now, (1) and (2) is a linear system in x and y.

(1) + (2) , we get

31x - 51y = 81

51x - 31y = 1

82x - 82y = 82

Dividing by 82, we get,

x - y = 1 ..... (3)

(1) - (2), we get

31x - 51y = 81

+51x + 31y = 1

20x + 20y = 80

Dividing by 20, we get

1x + 1y = 4 ....... (4)

Solving (3) ans (4) we get

x - y = 1

x + y = 4

2x = 5

x = $\frac{5}{2}$

x = 2.5

Substituting x = 2.5 in (3).

2.5 - y = 1

-y = 1- 2.5

-y = -1.5

y = 1.5

The system has two solutions is ( 2.5, 1.5 ).

Verifiction :

L.H.S. of (1) = 51x - 31y = 51(2.5) - 31(1.5) = 127.5 - 46.5 = 81 R.H.S. of (1)

L.H.S. of (2) = 31x - 51y = 31(2.5) + 51(1.5) = 77.5 - 76.5 = 1 R.H.S.of (2).

65x - 33y = 97, 33x - 65y = 1 ,

x = Answer: 2

y = Answer: 1

SOLUTION 1 :

This system is linear in x and y

33x + 65y = 97 ...... (1)

65x + 33y = 1 ..... (2)

Now, (1) and (2) is a linear system in x and y.

(1) + (2) , we get

33x - 65y = 97

65x - 33y = 1

98x - 98y = 98

Dividing by 98, we get,

x - y = 1 ..... (3)

(1) - (2), we get

33x - 65y = 97

+65x + 33y = 1

32x + 32y = 96

Dividing by 32, we get

1x + 1y = 3 ....... (4)

Solving (3) ans (4) we get

x - y = 1

x + y = 3

2x = 4

x = $\frac{4}{2}$

x = 2

Substituting x = 2 in (3).

2 - y = 1

-y = 1- 2

-y = -1

y = 1

The system has two solutions is ( 2, 1 ).

Verifiction :

L.H.S. of (1) = 65x - 33y = 65(2) - 33(1) = 130 - 33 = 97 R.H.S. of (1)

L.H.S. of (2) = 33x - 65y = 33(2) + 65(1) = 66 - 65 = 1 R.H.S.of (2).

58x - 28y = 85, 28x - 58y = 1 ,

x = Answer: 1.9

y = Answer: 0.9

SOLUTION 1 :

This system is linear in x and y

28x + 58y = 85 ...... (1)

58x + 28y = 1 ..... (2)

Now, (1) and (2) is a linear system in x and y.

(1) + (2) , we get

28x - 58y = 85

58x - 28y = 1

86x - 86y = 86

Dividing by 86, we get,

x - y = 1 ..... (3)

(1) - (2), we get

28x - 58y = 85

+58x + 28y = 1

30x + 30y = 84

Dividing by 30, we get

1x + 1y = 2.8 ....... (4)

Solving (3) ans (4) we get

x - y = 1

x + y = 2.8

2x = 3.8

x = $\frac{3.8}{2}$

x = 1.9

Substituting x = 1.9 in (3).

1.9 - y = 1

-y = 1- 1.9

-y = -0.9

y = 0.9

The system has two solutions is ( 1.9, 0.9 ).

Verifiction :

L.H.S. of (1) = 58x - 28y = 58(1.9) - 28(0.9) = 110.2 - 25.2 = 85 R.H.S. of (1)

L.H.S. of (2) = 28x - 58y = 28(1.9) + 58(0.9) = 53.2 - 52.2 = 1 R.H.S.of (2).

53x - 33y = 85, 33x - 53y = 1 ,

x = Answer: 2.6

y = Answer: 1.6

SOLUTION 1 :

This system is linear in x and y

33x + 53y = 85 ...... (1)

53x + 33y = 1 ..... (2)

Now, (1) and (2) is a linear system in x and y.

(1) + (2) , we get

33x - 53y = 85

53x - 33y = 1

86x - 86y = 86

Dividing by 86, we get,

x - y = 1 ..... (3)

(1) - (2), we get

33x - 53y = 85

+53x + 33y = 1

20x + 20y = 84

Dividing by 20, we get

1x + 1y = 4.2 ....... (4)

Solving (3) ans (4) we get

x - y = 1

x + y = 4.2

2x = 5.2

x = $\frac{5.2}{2}$

x = 2.6

Substituting x = 2.6 in (3).

2.6 - y = 1

-y = 1- 2.6

-y = -1.6

y = 1.6

The system has two solutions is ( 2.6, 1.6 ).

Verifiction :

L.H.S. of (1) = 53x - 33y = 53(2.6) - 33(1.6) = 137.8 - 52.8 = 85 R.H.S. of (1)

L.H.S. of (2) = 33x - 53y = 33(2.6) + 53(1.6) = 85.8 - 84.8 = 1 R.H.S.of (2).

10)

53x - 37y = 89, 37x - 53y = 1 ,

x = Answer: 3.25

y = Answer: 2.25

SOLUTION 1 :

This system is linear in x and y

37x + 53y = 89 ...... (1)

53x + 37y = 1 ..... (2)

Now, (1) and (2) is a linear system in x and y.

(1) + (2) , we get

37x - 53y = 89

53x - 37y = 1

90x - 90y = 90

Dividing by 90, we get,

x - y = 1 ..... (3)

(1) - (2), we get

37x - 53y = 89

+53x + 37y = 1

16x + 16y = 88

Dividing by 16, we get

1x + 1y = 5.5 ....... (4)

Solving (3) ans (4) we get

x - y = 1

x + y = 5.5

2x = 6.5

x = $\frac{6.5}{2}$

x = 3.25

Substituting x = 3.25 in (3).

3.25 - y = 1

-y = 1- 3.25

-y = -2.25

y = 2.25

The system has two solutions is ( 3.25, 2.25 ).

Verifiction :

L.H.S. of (1) = 53x - 37y = 53(3.25) - 37(2.25) = 172.25 - 83.25 = 89 R.H.S. of (1)

L.H.S. of (2) = 37x - 53y = 37(3.25) + 53(2.25) = 120.25 - 119.25 = 1 R.H.S.of (2).