The problem asks to solve the system of equations using substitution:

$y = -4x$ $y = 3x + 28$

Step 1: Substitute one equation into the other

Since both equations are equal to $y$, you can substitute $-4x$ from the first equation into the second equation:

$-4x = 3x + 28$

Step 2: Solve for $x$

Now, solve the equation for $x$:

$-4x - 3x = 28$ $-7x = 28$ $x = \frac{28}{-7} = -4$

Step 3: Solve for $y$

Now that we have $x = -4$, substitute this value back into either equation. Let's use $y = -4x$:

$y = -4(-4) = 16$

Final Solution:

The solution to the system is $(x, y) = (-4, 16)$.

Would you like more details or further clarification?

Here are five related questions to deepen your understanding:

1. Can you use the elimination method to solve the same system of equations?
2. What happens if both equations are parallel?
3. How do you solve systems of three equations with three variables?
4. What is the graphical interpretation of solving a system of equations?
5. How would the process change if one of the equations were quadratic?

Tip: Always double-check your solution by substituting the values back into the original equations to verify correctness.