I don't even know if this really falls into the category of modular arithmetic, but I wouldn't know what to call it since I don't have a formal math education.
Let’s say we know the resulting values of the following equations:
$$(x-a)\ \text{mod}(y-b)\equiv 4$$ $$(y-b)\ \text{mod} (x-a) \equiv -12$$ $$x \times y = 231$$ $$a \times b = 403$$
Is there any property of the modulus operations that would let me solve for all of the variables (a,b,x,y)?
*Edited with results for equations as an example.