Solution:

Given equations are ax by = a-b and bx-ay = ab.

We need to find the values of x and y that satisfy both of these equations.

Let's solve the equations one by one:

1. ax - by = a - b

We can rewrite this equation as:

ax - a = by - b

a(x - 1) = b(y - 1)

Dividing both sides by (x - 1) and (y - 1), we get:

a/b = y - 1 / x - 1

2. bx - ay = ab

We can rewrite this equation as:

bx - ab = ay

b(x - a) = ay

Dividing both sides by (x - a) and y, we get:

b/a = x - 1 / y

Now, we have two equations:

a/b = y - 1 / x - 1

b/a = x - 1 / y

We can solve for x and y using these two equations.

Multiplying both equations, we get:

y - 1 = x - 1

y = x

Substituting y = x in any of the two equations, we get:

a/b = 1

b/a = 1

Multiplying both equations, we get:

a^2 = b^2

Taking square root on both sides, we get:

a = +/- b

If a = b, then from equation (1), we get:

x - 1 = y - 1

x = y

Substituting x = y in equation (1), we get:

a(x - y) = a - b

a(0) = a - b

b = 0

But, b cannot be zero as it is present in the denominator in equation (2).

Therefore, a cannot be equal to b.

If a = -b, then from equation (1), we get:

x - 1 = -y + 1

x + y = 2

Substituting x + y = 2 in equation (1), we get:

a(2y - 2) = a - b

2a(y - 1) = a - b

2ay - 2a = a - b

2ay = 3a - b

Substituting a = -b, we get:

-2by = 3a + b

-2b(-a) = 3a - (-a)

2a = 4a

a = 0

Substituting a = 0 in equation (2), we get:

bx = 0

Since b cannot be zero, we have:

x = 0

Substituting x = 0 in equation (1), we get:

-aby = -b

y = 1

Therefore, the solution of the given equations is x = 0, y = 1.

But, this is not one of the options given.

Therefore, none of the options given is correct.

Hence, the given problem is incorrect.