Question

Solve:
(5/x+y)-(2/x-y) = -1,
(15/x+y)+(7/x-y)=10

Answer 1

The given equations are:

(5/x+y)-(2/x-y) = -1, .....(i)

(15/x+y)+(7/x-y)=10.....(ii)

Taking (1/x+y)= u and (1/x-y) = v

So, the given equations can also be written as_

5u-2v = -1....(iii)

15u+7v = 10....(iv)

Multiplying equation (iii) by 3

So we get,

(5u-2v)×3=-1×3

⇒ 15 u - 6v = -3....(v)

15u+7v = 10....(vi)

Subtracting equation (5) from (6), we have

13v = 13 ⇒ v=1

Substituting the value, v = 1 in (v)

15u-6×1 = -3 ⇒ 15u=-3+6=3 ⇒u = 3/15=1/5

Now,

u = 1/(x+y)=1/5

⇒ x+y = 5....(vii)

v = 1/(x-y)=1

⇒ x-y=1....(viii)

Adding equation(vii) and equation(viii), we have

2x = 6

⇒ x = 3

Substituting the value of x in (vii), we get

3+y = 5

⇒ y = 5-3

      = 2

Hence, the solution is x = 3, y = 2.

Answer 2

Answer:

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