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RD Chapter 8 Solution of Simultaneous Linear Equations Ex 8.1 Solutions

Question - 1 : -

Solve the following system of equations by matrix method:

(i) 5x + 7y + 2 = 0

4x + 6y + 3 = 0

(ii) 5x + 2y = 3

3x + 2y = 5

(iii) 3x + 4y – 5 = 0

x – y + 3 = 0

(iv) 3x + y = 19

3x – y = 23

(v) 3x + 7y = 4

x + 2y = -1

(vi) 3x + y = 7

5x + 3y = 12

Answer - 1 : -

(i) Given 5x + 7y + 2= 0 and 4x + 6y + 3 = 0

Hence, x = 9/2and y = -7/2

(ii) Given 5x + 2y = 3

3x + 2y = 5

Hence, x = -1and y = 4

(iii) Given 3x + 4y –5 = 0

x – y + 3 = 0

Hence, X = 1 Y = – 2

(iv) Given 3x + y = 19

3x – y = 23

(v) Given 3x + 7y = 4

x + 2y = -1

(vi) Given 3x + y = 7

5x + 3y = 12

Question - 2 : - Solve the following system of equations by matrix method:

(i) x + y –z = 3
2x + 3y + z = 10
3x – y – 7z = 1

(ii) x + y + z = 3

2x – y + z = -1

2x + y – 3z = -9

(iii) 6x – 12y + 25z = 4

4x + 15y – 20z = 3

2x + 18y + 15z = 10

(iv) 3x + 4y + 7z = 14

2x – y + 3z = 4

x + 2y – 3z = 0

(v) (2/x) – (3/y) + (3/z) = 10

(1/x) + (1/y) + (1/z) = 10

(3/x) – (1/y) + (2/z) = 13

(vi) 5x + 3y + z = 16

2x + y + 3z = 19

x + 2y + 4z = 25

(vii) 3x + 4y + 2z = 8

2y – 3z = 3

x – 2y + 6z = -2

(viii) 2x + y + z = 2

x + 3y – z = 5

3x + y – 2z = 6

(ix) 2x + 6y = 2

3x – z = -8

2x – y + z = -3

(x) 2y – z = 1

x – y + z = 2

2x – y = 0

(xi) 8x + 4y + 3z = 18

2x + y + z = 5

x + 2y + z = 5

(xii) x + y + z = 6

x + 2z = 7

3x + y + z = 12

(xiii) (2/x) + (3/y) + (10/z) = 4,

(4/x) – (6/y) + (5/z) = 1,

(6/x) + (9/y) – (20/z) = 2, x, y, z ≠ 0

(xiv) x – y + 2z = 7

3x + 4y – 5z = -5

2x – y + 3z = 12

Answer - 2 : - (i)


(ii)

(iii)
(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

(xi)

(xii)

(xiii)

(xiv)

Question - 3 : -

Show that each one of the following systems of linear equations isconsistent and also find their solutions:

(i) 6x + 4y = 2

9x + 6y = 3

(ii) 2x + 3y = 5

6x + 9y = 15

(iii) 5x + 3y + 7z = 4

3x + 26y + 2z = 9

7x + 2y + 10z = 5

(v) x + y + z = 6

x + 2y + 3z = 14

x + 4y + 7z = 30

(vi) 2x + 2y – 2z = 1

4x + 4y – z = 2

6x + 6y + 2z = 3

Answer - 3 : - (i)


(ii)

(iii)

(iv)

(v)

(vi)

Question - 4 : -

Show that each one of the following systems of linear equations isconsistent:

(i) 2x + 5y = 7

6x + 15y = 13

(ii) 2x + 3y = 5

6x + 9y = 10

(iii) 4x – 2y = 3

6x – 3y = 5

(iv) 4x – 5y – 2z = 2

5x – 4y + 2z = -2

2x + 2y + 8z = -1

(v) 3x – y – 2z = 2

2y – z = -1

3x – 5y = 3

(vi) x + y – 2z = 5

x – 2y + z = -2

-2x + y + z = 4

Answer - 4 : - (i)


(ii)
(iii)

(iv)

(v)

(vi)

Question - 5 : -

Answer - 5 : -


Question - 6 : -

Answer - 6 : -


Question - 7 : -

Answer - 7 : -


Question - 8 : -
1.
2.
3.
4.

Using A-1,solve the system of linear equations X - 2y = 10, 2x + y + 3z = 8 and -2y + z = 7

5.

Answer - 8 : - 1.

2.
3.
4.
5.

Question - 9 : -

Answer - 9 : -


Question - 10 : -

An amount of ₹10,000 is put into three investments at the rate of 10, 12and 15% per annum. The combined incomes are ₹1310 and the combined income offirst and second investment is ₹ 190 short of the income from the third. Findthe investment in each using matrix method.

Answer - 10 : -


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