Solve the following system of equations:(x + y)/xy = 2; (x – y)/xy

1.	Solve the following system of equations:(x + y)/xy = 2; (x – y)/xy = 6
Answer» The given pair of equations are: (x + y)/xy = 2 ⇒ 1/y + 1/x = 2……. (i) (x – y)/xy = 6 ⇒ 1/y – 1/x = 6………(ii) Let 1/x = u and 1/y = v, so the equation (i) and (ii) becomes v + u = 2……. (iii) v – u = 6……..(iv) Adding (iii) and (iv), we get 2v = 8 ⇒ v = 4 ⇒ y = 1/v = \(\frac{1}{4}\) Substituting v = 4 in (iii) to find x, 4 + u = 2 ⇒ u = -2 ⇒ x = 1/u = -\(\frac{1}{2}\) Hence, the solution is x = -\(\frac{1}{2}\) and y = \(\frac{1}{4}\).

Solve the following system of equations:(x + y)/xy = 2; (x – y)/xy = 6

Answer»

The given pair of equations are:

(x + y)/xy = 2

⇒ 1/y + 1/x = 2……. (i)

(x – y)/xy = 6

⇒ 1/y – 1/x = 6………(ii)

Let 1/x = u and 1/y = v, so the equation (i) and (ii) becomes

v + u = 2……. (iii)

v – u = 6……..(iv)

Adding (iii) and (iv), we get

2v = 8

⇒ v = 4

⇒ y = 1/v = \(\frac{1}{4}\)

Substituting v = 4 in (iii) to find x,

4 + u = 2

⇒ u = -2

⇒ x = 1/u = -\(\frac{1}{2}\)

Hence, the solution is x = -\(\frac{1}{2}\) and y = \(\frac{1}{4}\).