Question

Do by cross multiplication:-
5/(x+y) - 2/(x-y) + 1 =0 ,
15/(x+y) + 7(x-y) - 10 = 0 ( x≠y , x≠-y )​

Answer 1

Step-by-step explanation:

The given equations are

5/ x+y - 2/ x-y = -1 ……(i)

15/ x+y - 7/x-y= 10 ……(ii)

Substituting 1/x+y = u and 1/x-y = v in (i) and (ii), we get

5u – 2v = -1 ……..(iii)

15u + 7v = 10 …….(iv)

Multiplying (iii) by 3 and subtracting it from (iv), we get

7v + 6v = 10 + 3

⇒13v = 13

⇒v = 1

⇒x – y = 1 (∵ 1/ x-y = ) …..(v)

Now, substituting v = 1 in (iii), we get

5u – 2 = -1

⇒5u = 1

⇒u = 1/ 5

x + y = 5 …….(vi)

Adding (v) and (vi), we get

2x = 6

⇒ x = 3

Substituting x = 3 in (vi), we have

3 + y = 5 ⇒ y = 5 – 3 = 2

Hence, x = 3 and y = 2.