To simplify the expression:

$4 - 5 - 2x - 4y + 4 - 5x + 7y$

Let's group the constants, the terms involving $x$, and the terms involving $y$:

Step 1: Combine the constants

$4 - 5 + 4 = 3$

Step 2: Combine the $x$-terms

$-2x - 5x = -7x$

Step 3: Combine the $y$-terms

$-4y + 7y = 3y$

Final Expression:

$3 - 7x + 3y$

So, the simplified expression is:

$3 - 7x + 3y$

Would you like further explanation on any part of the process?

Here are some related questions:

1. How do you simplify an expression with more variables?
2. What is the distributive property and how does it apply here?
3. How would you factor out common terms from an expression?
4. What are like terms, and how do you combine them?
5. How do coefficients affect the simplification of algebraic expressions?

Tip: When simplifying algebraic expressions, always group like terms first (those with the same variables and exponents).