Coordinate System Transformation

Problem Description

You are tasked with implementing a critical part of a high-precision geometry engine. Your goal is to transform a 2D point from a local coordinate system to a global one.

The output must satisfy the following goal relative to the input (x, y):

• The global X coordinate must be exactly 2*x + 10.
• The global Y coordinate must be exactly 3*y - 5.

You must implement a function transform_coordinates(x, y) that achieves this state.

Requirements:

• To ensure traceability and precision, do NOT calculate the final values in a single expression.
• Use a sequence of distinct assignments to calculate the final X and Y.
• You must include a rigorous derivation in the code's comments to prove that the sequence of assignments you've chosen logically guarantees the required output for all valid inputs.

Output Specification

Produce a Python file geometry.py containing the transform_coordinates function. The function must be robust and include the step-by-step logical justification in the comments.