10th cbse maths solution for exercise 3.6 part 2

This page 10th cbse maths solution for exercise 3.6 part 2 is going to provide you solution for every problems that you find in the exercise no 3.6

10th CBSE maths solution for Exercise 3.6 part 2

(iv) 5/(x – 1) + 1/(y – 2) = 2

       6/(x – 1) – 3/(y – 2) = 1

Solution:

Let 1/(x – 1) = a and 1/(y – 2) = b

5 a + b = 2  --------(1)

6 a – 3 b = 1  --------(2)

 (1) x 3 => 15 a + 3 b = 6

                     6 a – 3 b = 1

                   -----------------      

                      21 a = 7

                           a = 7/21

                           a = 1/3

1/(x-1) = 1/3

3 = x -1

x – 1 = 3

 x = 3 + 1

 x = 4 

Substitute a = 1/3 in the first equation

5(1/3) + b = 2

(5/3 )+ b = 2

           b =  2 – (5/3)

          b = 1/3

1/(y – 2) = 1/3

3 = y – 2

y – 2 = 3

 y = 3 + 2

 y = 5


(v)  (7 x - 2 y)/xy = 5

     (8 x + 7 y)/xy = 15

Solution:

  (1) x 7 = > - 14 a + 49 b = 35

  (2) x 2 = >  14 a + 16 b = 30

                   -----------------------       

                             65 b = 65

                                 b = 1

Substitute b = 1 in the first equation

-2 a + 7 (1) = 5

 -2a + 7 = 5

      - 2a = 5 -7

       -2a = -2

         a = 1

1/x = a             1/ y = b

1/x = 1             1/y = 1

x = 1       y = 1


(vi) 6 x + 3 y = 6 xy

       2 x + 4 y = 5 xy

Solution:

Dividing the whole equation by xy

    (6 x/xy) + (3y/xy) = (6xy/xy)

    (2x/xy) + (4y/xy) = (5xy/xy) 

     (6/y) + (3/x) = 6

       (2/y) + (4/x) = 5

1/x = a and 1/y = b

   3 a + 6 b = 6  ---------(1)

   4 a + 2 b = 5  ---------(2)

                 3 a + 6 b = 6

(2) x 3 =>12 a + 6 b =  15

                 (-)      (-)       (-)

             ---------------------

                   -9a  = - 9

                       a = 1

Substitute a = 1 in the first equation

3(1) + 6 b = 6

3 + 6 b = 6

       6 b = 6 – 3

       6 b = 3

     b = 3/6

      b = 1/2

1/x = a            1/y = b

1/x = 1             1/y = 1/2

x = 1                   y = 2

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