Sir please give me a detailed solution of this question as it was already asked in various examinations in which we have been asked to find the value of variables x and y from the equations 9/x-4/y=8, 13/x+7/y=101
RS Aggarwal, class 10, chapter 3B, question no 22
The given equations are:
9/x – 4/y = 8 ……..(i)
13/x + 7/y = 101 ……..(ii)
Putting 1/x = u and 1/y = v, we get: 9u – 4v = 8 …….(iii)
13u + 7v = 101 ……(iv)
On multiplying (iii) by 7 and (iv) by 4, we get:
63u – 28v = 56 ……..(v)
52u + 28v = 404 ……..(vi)
On adding (v) from (vi), we get: 115u = 460
⇒ u = 4
⇒ 1/ x = 4
⇒ x = 1/4
On substituting x = 1/ 4 in (i), we get:
9/ 1/ 4 – 4/ y = 8
⇒36 – 4/ y = 8
⇒ 4/ y = (36 – 8) = 28 y = 4/ 28 = 1/7 Hence, the required solution is x = 1/4 and y = 1/ 7.