To solve for $x$ and $y$ using the Pythagorean theorem and ratios, we need more information. The Pythagorean theorem relates the sides of a right triangle, while ratios could be referring to the relationship between these sides or angles.

Could you please provide more context or an equation or diagram that involves $x$ and $y$ in the context of the Pythagorean theorem and ratios? This will help me understand the problem better and provide a precise solution.