1. **State the problem:** Find the domain of the function $$f(x,y) = \frac{xy}{y - 2x}$$. 2. **Recall the domain rule:** The domain of a function includes all input values for which the function is defined. 3. **Identify restrictions:** The denominator cannot be zero because division by zero is undefined. 4. **Set denominator not equal to zero:** $$y - 2x \neq 0$$ 5. **Solve for y:** $$y \neq 2x$$ 6. **Interpretation:** The function is defined for all real numbers $$x$$ and $$y$$ except where $$y = 2x$$. 7. **Final answer:** The domain is all $$(x,y) \in \mathbb{R}^2$$ such that $$y \neq 2x$$.