Let's analyze and simplify the given expression:

$-1 + 1 + 4y + 2x + 4 - 5y$

Step-by-step simplification:

1. Combine the constant terms: $-1 + 1 + 4 = 4$

2. Combine the $y$-terms: $4y - 5y = -y$

3. The $x$-term stays as it is: $2x$

Final simplified expression:

$4 + 2x - y$

Let me know if you'd like further details or have any questions!

Related Questions:

1. What are like terms and why do we combine them?
2. How would the expression change if one of the terms had a higher power (e.g., $y^2$)?
3. How do coefficients affect the combination of like terms?
4. What if we had a division or multiplication in the expression?
5. How can we simplify expressions that involve more variables?

Tip: Always group like terms (terms that have the same variable and exponent) to simplify expressions easily.