I can understand how the Greek alphabet came to be prominent in mathematics as the Greeks had a huge influence in the math of today. Certain letters came to have certain implications about their meaning (i.e. $\theta$ is almost always an angle, never a function).
But why did $x$ and $y$ come to prominence? They seem like $2$ arbitrary letters for input and output, and I can't think why we began to use them instead of $a$ and $b$. Why did they become the de facto standard for Cartesian coordinates?