Answer
The limit does not exist
Work Step by Step
Consider $f(x,y)=\dfrac{x^2-y}{x-y}$
Let us consider the approach: $(x,y) \to (0,0)$ along $y=mx; m\ne 1$
Then, we get $\lim\limits_{x \to 0}\dfrac{x^2-mx}{x-mx}=\dfrac{-k}{1-k}$
This shows us that there are multiple limit values when the approach is different and therefore, the limit does not exist for the given function.