Question

15/x+y-2/x-y=-1 15/x+y+7/x-y=10 where x is not = 0,y is not = 0

Answer 1

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.