Solve the following simultaneous linear equations:

ax + by = a - b

bx - ay = a + b

Given,

ax + by = a - b …….(i)

bx - ay = a + b …….(ii)

Multiplying eq. (i) by b and (ii) by a we get,

abx + b²y = ab - b² ……(iii)

abx - a²y = a² + ab …….(iv)

Subtracting eq. (iv) from (iii),

⇒ abx + b²y - (abx - a²y) = ab - b² - (a² + ab)

⇒ b²y + a²y = -b² - a²

⇒ y(b² + a²) = -(b² + a²)

⇒ y = -1.

Substituting value of y in (i),

⇒ ax + b(-1) = a - b

⇒ ax - b = a - b

⇒ ax = a - b + b

⇒ ax = a

⇒ x = 1.

Hence, x = 1 and y = -1.