Coordinate geometry

I tried setting these up as simultaneous equations:

y = ax + 1 / b -> by = abx + 1 -> abx - by = -1

y = bx + 1 / a -> ay = abx + 1 -> abx - ay = -1

Now, subtracting the second one from the first one, I get:

abx - by = -1

-abx + ay = 1

Adding them together, I get:

(a - b)y = 0

This means either:

y = 0 -> not one of the above choices

or

a - b = 0 -> a = b -> which is contrary to the instructions for the problem (Given a is not equal to b)

Are you sure you have stated everything correctly?

Yeah , I am 100% sure

Then I must be doing something wrong that I didn't discover even looking over it a second time. Incidentally, I edited my response to show that I subtracted the second one from the first (I had originally written that I had subtracted the first one from the second even though I had done the opposite), plus I showed the x terms in the intermediate results.

Maybe someone else here can see the way to the proper solution. Or if this was given to you by a teacher, see if this person knows what to do.

May be option of answer is wrong?

Do you mean that 0 should have been one of the choices? I think it should have been.

OR, 1 is near to zero rather than other . so a is answer

Here's another question.

If the circle is translated three units to the up and three units to the right and the radius increased by 2 units , what will be the equation of the circle?

a) x^2+(y-7)^2=36

b) (x-7)^2+(y-4)^2=36

c) (x-7)^2+y^2=100

d) (x+1)^2+y^2=100