NCERT Solutions For Class 10 Math Chapter – 3 Exercise – 3.6

NCERT Solutions For Class 10 Math Chapter – 3 Exercise – 3.6

Q1. Solve the following pairs of linear equation by reducing them to a pair of linear equations:

1/2x + 1/3y = 2

1/3x + 12y = 13/6

2/√x + 3/√y = 2

4/√x – 9/√y = -1

4/x + 3y = 14

3/x – 4y = 23

5/x-1 + 1/y – 2 = 2

6/x- 1 – 3/y – 2 = 1

7x – 2y/xy = 5

8x + 7y /xy = 15

6x + 3y = 6xy

2x + 4y = 5xy

10/x + y + 2/x – y = 4

15/x + y – 5/x – y = -2

1/3x + y + 1/3x – y = 3/4

1/2(3x + y) – 1/2(3x – y) = -1/8

Solution:-

3a + 2b = 12 (I)

2a + 3b = 13 (ii)

Solving (I) and (ii) we get

A = 2 , b = 3

X = 1/2 , y = 1/3

2a + 3b = 2 (I)

4a – 9b = -1 (ii)

Solving (I) and (ii) we get a = 1/2 , b = 1/3

A = 1/2 = 1/√x = 1/2

√x = 2 = x = 4

B = 1/3 = 1/√y = 1/3

√y = 3 y = 9

4a + 3y = 14 (I)

3a – 4y = 23 (ii)

Solving for a and y we get

A = 5 y = -2

1/x = 5 and y = -2

X = 1/5 y = -2

5a+ b = 2 (I)

6a – 3 = 1 (ii)

Solving (I)) and (ii) we get

A = 1/3 , b = 1/3

1/x-1 = 1/3 and 1/y – 2 = 1/3

X = 4 and y = 5 is the solution,

7/y – 2/x = 5 (I)

8/y + 7/x = 15 (ii)

7b – 2a = 5 (I)

8b + 7a = 15 (ii)

Solving for a , b we get

A = 1 and b = 1

1/x = 1 and 1/y = 1

X = 1 and y = 1 is the solutions.

6/y + 3/x = 6

2x + 4y = 5xy

2/y + 4/x = 5

Let 1/x = a , 1/y = b.

From (I) and (ii) we get

6b + 3a = 6 (iii)

2b + 4a = 5 (iv)

Solving (iii) and (iv) we get a = 1 , b = 1/2

A = 1 = 1/x = 1 x = 1

B = 1/2 1/y = 1/2 = y= 2

10a + 2b = 4 (I)

15a – 5b = -2 (ii)

Solving (I) and (ii) we get a = 1/5 b = 1

A = 1/5 = 1/x + y = 1/5 = x + y = 5 (iii)

B = 1 1/x-y = 1 = x – y = 1 (iv)

Solving (iii) and (iv) we get x = 3 , y = 2

4a + 4b = 3 (I)

4a – 4b = -1 (ii)

Solving (I) and (ii) we get a = 1/4 , b = 1/2

A = 1/4 = 1/3x + y = 1/4

3x + y = 4 (iii)

B = 1/22 = 1/3x – y = 1/2

3x – y = 2 (iv)

Solving (iii) and (iv) we get x = 1 , y = 1.

Q2. Formulate the following problems as a pair of equations . and hence find their solutions:

Ritu can row downstream 20 km in 2 hours , and upstream 4 km in 2 hours . Find her speed of rowing in still water and the speed of the current.
2 women and 5 men can together finish an embroidery work in 4 days while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 women alone to finish the work, and also that taken by 1 man alone.
Roohi travels 300 km to her home partly by train and party by Bus She takes 4 hours if she travels 60 km by train and the remaining by bus, she takes 10 minute longer . Find the speed of the train and the bus separately.

Solution:-