To solve this system of equations using substitution, let's follow these steps:

We are given:

1. $y = 2x + 14$
2. $5x - 2y = -33$

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

Substitute $y = 2x + 14$ into the second equation:

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

Step 2: Simplify and solve for $x$.

Distribute the $-2$ across the terms inside the parentheses:

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

Now simplify:

$x - 28 = -33$

Add 28 to both sides:

$x = -33 + 28$

$x = -5$

Step 3: Substitute $x = -5$ back into the first equation to find $y$.

Now, substitute $x = -5$ into $y = 2x + 14$:

$y = 2(-5) + 14$

$y = -10 + 14$

$y = 4$

Solution:

The solution to the system is $x = -5$ and $y = 4$.

Would you like more details or explanations on this method? Feel free to ask!

Here are 5 related questions:

1. How do you determine which variable to substitute first?
2. Could this system of equations be solved graphically instead?
3. What happens if both equations are solved using elimination instead of substitution?
4. How do we verify if the solution is correct?
5. What are some common mistakes when solving systems of equations by substitution?

Tip: Always simplify both equations as much as possible before starting substitution.