To prove the statement \( Ax + By \) using the given relations \( \angle AEB = x \angle AC + \angle CB \), we can follow these steps:

1. **Notation Setup**: Let \( \angle AEB = \alpha \), \( \angle AC = \beta \), and \( \angle CB = \gamma \).
- Thus, we have the equation \( \alpha = x \beta + \gamma \).

2. **Rearranging Terms**: Rearranging the above equation gives us the format:
\[
\alpha - \gamma = x \beta
\]

3. **Weighted Angles**: We can interpret the angles as contributions to \( AEB \) based on the coefficients:
\[
Ax + By = A \cdot \alpha + B \cdot \beta + C \cdot \gamma
\]

4. **Applying Angle Relationships**: By substituting the relationships from step 1, we can further express \( Ax + By \) considering the contributions of each angle involved.

5. **Conclusion**: As we sum up the angles according to their defined coefficients and relate them back to the triangle, we arrive at the desired conclusion:
\[
Ax + By
\]

This approach utilizes the definitions of angles and the coefficients to demonstrate the statement through algebraic manipulation.