(Q5). Solve the given equation.

ax
b
 +
by
a
 = a + b

ax – by = 2ab

Given:
ax
b
 +
by
a
 = a + b ................(1)

ax – by = 2ab …….. (2)

equation (1) × ⇒ ax -
2
a
 y = (a+b)
equation (2)      ⇒ ax – y = ab
y(-
2
a
) = a + 2 - ab

= (2 - a)

∴ y = (2 - a)(
a
a - 2
 ) = -

Substituting y = – in equation (2)

we get ax – b(-) = 2ab

ax + b = 2ab

ax = 2ab – b = b

⇒ x =
b
a
 =

∴ (x, y) = (, -)