Solve for x and y:5/x+y - 2/x-y = -115/x+y - 7/x-y = 10

1.	Solve for x and y:5/x+y - 2/x-y = -115/x+y - 7/x-y = 10
Answer» 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.

Answer»

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.

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