Solve for x and y:\(\frac{5}{x+y}-\frac{2}{x-y}=-1\),\(\frac{15}{x+y}-

1.	Solve for x and y:\(\frac{5}{x+y}-\frac{2}{x-y}=-1\),\(\frac{15}{x+y}-\frac{7}{x-y}=10\)
Answer» The given equations are \(\frac{5}{x+y}-\frac{2}{x-y}=-1\).......(i) \(\frac{15}{x+y}-\frac{7}{x-y}=10\)......(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 \((∵\frac{1}{x-y}=v)\)......(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.

Solve for x and y:\(\frac{5}{x+y}-\frac{2}{x-y}=-1\),\(\frac{15}{x+y}-\frac{7}{x-y}=10\)

Answer»

The given equations are

\(\frac{5}{x+y}-\frac{2}{x-y}=-1\).......(i)

\(\frac{15}{x+y}-\frac{7}{x-y}=10\)......(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 \((∵\frac{1}{x-y}=v)\)......(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.