1. **State the problem:** Solve for $x$ and $y$ in the equation $$\frac{635}{10} = \left(63 \cdot \frac{x}{100}\right) + \left(65 \cdot \frac{y}{100}\right).$$ 2. **Rewrite the equation:** Simplify the left side and rewrite the right side: $$63.5 = 0.63x + 0.65y.$$ 3. **Isolate terms:** This is a linear equation in two variables $x$ and $y$. Without additional information or another equation, we cannot find unique values for $x$ and $y$. 4. **Interpretation:** Usually, such problems require either a second equation or a condition relating $x$ and $y$ to solve uniquely. 5. **Summary:** The equation relates $x$ and $y$ as: $$0.63x + 0.65y = 63.5.$$ Without more data, the solution is the set of all $(x,y)$ pairs satisfying this linear equation.