(Q5).Solve each of the following pairs of equations by reducing them to a pair of linear equations.

x+y
xy
 = 2;
x-y
xy
 = 6

Given

x+y
xy
 = 2
⇒
xy
 +
xy
 = 2
⇒
1
 +
1
 = 2
x-y
xy
 = 6
⇒
xy
 -
xy
 = 6
⇒
1
 -
1
 = 6
Take
1
x
 = and
1
y
 = ,

then the given equations reduces to

+ = 2 ……… (1)

- + = 6 ………. (2)

b =
⇒ b =
=

Substituting b = in equation (1) we get

a + = 2 ⇒ a = 2 – = -

but a =
1
x
 = - ⇒ x =
-1
b =
1
y
 = ⇒ y =
1
∴ Solution (x, y) = (
- 1
,
1
)