We are asked to solve this system of equations using substitution:

y = 2x + 14 \tag{1} 5x - 2y = -33 \tag{2}

Step 1: Substitute $y$ from equation (1) into equation (2).

From equation (1), we know that $y = 2x + 14$. We will substitute this into equation (2):

$5x - 2(2x + 14) = -33$

Step 2: Simplify the equation.

Distribute the $-2$ on the left side:

$5x - 4x - 28 = -33$

Combine like terms:

$x - 28 = -33$

Step 3: Solve for $x$.

Add 28 to both sides:

$x = -33 + 28$ $x = -5$

Step 4: Substitute $x = -5$ back into equation (1).

Now that we know $x = -5$, substitute it into equation (1) to find $y$:

$y = 2(-5) + 14$ $y = -10 + 14$ $y = 4$

Final Solution:

The solution to the system is: $x = -5, \quad y = 4$

Would you like further clarification on any step or additional details?

Here are 5 related questions to expand on this problem:

1. How would you solve the system of equations using the elimination method?
2. Can you graph the two equations and verify the solution visually?
3. What happens if you use substitution with different forms of the equation?
4. How does the substitution method work for non-linear systems of equations?
5. How would this problem change if the second equation had been $5x + 2y = -33$?

Tip: When solving systems of equations, always ensure that you correctly substitute the variable, and carefully simplify to avoid mistakes in algebraic manipulation.