(Q10).Solve each of the following pairs of equations by reducing them to a pair of linear equations.

10
x+y
 +
2
x-y
 = 4
15
x+y
 +
5
x-y
 = -2

Given

10
x+y
 +
2
x-y
 = 4 and
15
x+y
 +
5
x-y
 = -2
Take
1
x+y
 = and
1
x-y
 = , then

the given equations reduce to

a + b = 4 ……… (1)

a – b = – 2 ……… (2)

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

Substituting b = in equation (1) we get

10a + 2() = 4

⇒ 10a = 4 –

⇒ a =
10
 =
but a =
1
x+y
 =
1
 ⇒ x + y = ……. (3)
b =
1
x-y
 = ⇒ x - y = ............(4)

Adding (3) and (4)

x + y =

x - y =

x =
⇒ x =
=

Substituting x = in x + y = 5 we get

+ y = 5 ⇒ y = 5 – =

∴ Solution (x, y) = (, )