Given that 6(ax + by) = 3a + 2b

6ax + 6by = 3a + 2b ——— (1)

6(bx – ay) = 3b – 2a

6bx – 6ay = 3b – 2a ————- (2)

On solving (1) a & (2) b, we get

6ax 2 + 6aby = 3a 2 + 2ab

6b 2 x – 6aby = 3b 2 – 2ab

—————————————

6ax^2 + 6b 2 x = 3a^2 + 3b^2

6x(a^2 + b^2) = 3(a^2 + b^2)

x = 3/6 x = 1/2.

Substitute x = 1/2 in above equations,

we get

6ax + 6by = 3a + 2b

6a(1/2) + 6by = 3a + 2b

3a + 6by = 3a + 2b

6by = 2b

y = 2b/6b

y = 1/3.

Therefore the value of x = 1/2 and y = 1/3.