This question is taken from linear equations in two variables in which we have to find the value of variables x and y from the equations 4x+6y=3xy, 8x+9y=5xy

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 3B, question no 25

The given equations are:

4x + 6y = 3xy …..(i)

8x + 9y = 5xy ……(ii)

From equation (i), we have:

4x + 6y/ xy = 3

⇒ 4/y + 6/x = 3 ……(iii)

For equation (ii), we have:

8x + 9y/ xy = 5

⇒ 8/y + 9/x = 5 ……(iv)

On substituting 1/y = v and 1/x = u, we get:

4v + 6u = 3 ……(v)

8v + 9u = 5 …….(vi)

On multiplying (v) by 9 and (vi) by 6, we get:

36v + 54u = 27 ….(vii)

48v + 54u = 30 ….(viii)

On subtracting (vii) from (viii), we get:

12v = 3

⇒ v = 3/12 = 1/4

⇒ 1/ y = 1/4

⇒ y = 4 On substituting y =4 in (iii), we get:

4/4 + 6/x= 3

⇒ 1 + 6/x = 3

⇒ 6/x = (3 – 1) = 2

⇒ 2x = 6

⇒ x = 6/2 = 3

Hence, the required solution is x = 3 and y = 4.