1. **State the problem:** Simplify the algebraic expression $9x - 4y + 2x - y - 6x + 5y$. 2. **Identify like terms:** Like terms are terms that have the same variable raised to the same power. Here, the like terms are those with $x$ and those with $y$. 3. **Group like terms:** $$9x + 2x - 6x - 4y - y + 5y$$ 4. **Combine like terms:** For $x$ terms: $$9x + 2x - 6x = (9 + 2 - 6)x = 5x$$ For $y$ terms: $$-4y - y + 5y = (-4 - 1 + 5)y = 0y = 0$$ 5. **Write the simplified expression:** $$5x + 0 = 5x$$ **Final answer:** $5x$