Solve for x and y:\(\frac{10}{x+y}+\frac{2}{x-y}=4\),\(\frac{15}{x+y}-

1.	Solve for x and y:\(\frac{10}{x+y}+\frac{2}{x-y}=4\),\(\frac{15}{x+y}-\frac{9}{x-y}=-2\),where x ≠ y, x ≠ -y.
Answer» The given equations are \(\frac{10}{x+y}+\frac{2}{x-y}=4\).............(i) \(\frac{15}{x+y}-\frac{9}{x-y}=-2\).......(ii) Substituting 1/x+y = u and 1/x−y = v in (i) and (ii), we get: 10u + 2v = 4 ……..(iii) 15u - 9v = -2 …….(iv) Multiplying (iii) by 9 and (iv) by 2 and adding, we get: 90u + 30u = 36 – 4 ⇒120u = 32 ⇒u = 32/120 = 4/15 ⇒x + y = 15/4 \((∵\frac{1}{x+y}=u)\).........(v) On substituting u = 4/15 in (iii), we get: 10 × 4/15 + 2v = 4 8/3 + 2v = 4 ⇒2v = 4 - 8/3 = 4/3 ⇒v = 2/3 ⇒ x – y = 3/2 \((∵\frac{1}{x-y}=v)\)........(vi) Adding (v) and (vi), we get 2x = 15/4 + 3/2 ⇒2x = 21/4 ⇒x = 21/8 Substituting x = 21/8 in (v), we have 21/8 + y = 15/4 ⇒y = 15/4 - 21/8 = 9/8 Hence, x = 21/8 and y = 9/8

Solve for x and y:\(\frac{10}{x+y}+\frac{2}{x-y}=4\),\(\frac{15}{x+y}-\frac{9}{x-y}=-2\),where x ≠ y, x ≠ -y.

Answer»

The given equations are

\(\frac{10}{x+y}+\frac{2}{x-y}=4\).............(i)

\(\frac{15}{x+y}-\frac{9}{x-y}=-2\).......(ii)

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

10u + 2v = 4 ……..(iii)

15u - 9v = -2 …….(iv)

Multiplying (iii) by 9 and (iv) by 2 and adding, we get:

90u + 30u = 36 – 4

⇒120u = 32

⇒u = 32/120 = 4/15

⇒x + y = 15/4 \((∵\frac{1}{x+y}=u)\).........(v)

On substituting u = 4/15 in (iii), we get:

10 × 4/15 + 2v = 4

8/3 + 2v = 4

⇒2v = 4 - 8/3 = 4/3

⇒v = 2/3

⇒ x – y = 3/2 \((∵\frac{1}{x-y}=v)\)........(vi)

Adding (v) and (vi), we get

2x = 15/4 + 3/2 ⇒2x = 21/4 ⇒x = 21/8

Substituting x = 21/8 in (v), we have

21/8 + y = 15/4 ⇒y = 15/4 - 21/8 = 9/8

Hence, x = 21/8 and y = 9/8