We have,

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

⇒ 6ax + 6by = 3a + 2b …(i)

6(bx – ay) = 3b – 2a

⇒ 6bx – 6ay = 3b – 2a …(ii)

To solve these equations, we need to make one of the variables (in both the equations) have same coefficient.

Lets multiply equation (i) by a and (ii) by b, so that variable y in both the equations have same coefficient.

Recalling equations 1 & 2,

6ax + 6by = 3a + 2b [×a]

6bx – 6ay = 3b – 2a [×b]

⇒ 6a²x + 6b²x + 0 = 3a² + 3b²

⇒ 6(a² + b²)x = 3(a² + b²)

⇒ 2x = 1

⇒ x = 1/2

Substitute x = 1/2 in equations (i)/(ii), as per convenience of solving.

Thus, substituting in equation (i), we get

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

⇒ 3a + 6by = 3a + 2b

⇒ 6by = 2b

⇒ y = 1/3

Hence, we have x = 1/2 and y = 1/3.