(Q8).Solve each of the following pairs of equations by reducing them to a pair of linear equations.

5
x+y
 -
2
x-y
 = - 1
15
x+y
 +
7
x-y
 = 10

where x ≠ 0, y ≠ 0

Given

5
x+y
 -
2
x-y
 = - 1 and
15
x+y
 +
7
x-y
 = 10
Take
1
x+y
 = and
1
x-y
 = , then

the given equations reduce to

a – b = – 1 ……… (1)

a + b = 10 ……… (2)

equation (1) × ⇒ a - b = -
equation (2)      ⇒ a + b =
-b = -
⇒ b =
-
-
 =

Substituting b = in equation (1) we get

5a – 2() = -1

⇒ 5a = -1 +

⇒ 5a =

⇒ a =
but a =
1
x+y
 =
1
 ⇒ x + y =
b =
1
x-y
 = ⇒ x – y =
⇒ x =
=

Solving the above equations

Substituting x = in x + y = 5 we get

+ y = 5 ⇒ y = 5 – =

∴ Solution (x, y) = (, )