Solve for x and y: 9/x - 4/y = 8, 13/x + 7/y = 101

1.	Solve for x and y: 9/x - 4/y = 8, 13/x + 7/y = 101
Answer» 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.

Answer»

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.

Discussion