The system of equations provided in the image is:

$x = 2y$ $-9x + 4y = 28$

Step-by-Step Solution:

1. Substitute the first equation $x = 2y$ into the second equation $-9x + 4y = 28$.

   $-9(2y) + 4y = 28$

2. Simplify the equation:

   $-18y + 4y = 28$

   Combine like terms:

   $-14y = 28$

3. Solve for $y$:

   $y = \frac{28}{-14} = -2$

4. Now that we know $y = -2$, substitute it back into the first equation $x = 2y$ to find $x$:

   $x = 2(-2) = -4$

Solution:

The solution to the system of equations is: $x = -4, \quad y = -2$

Would you like further details or explanations on any part of this process?

Here are 5 related questions to deepen your understanding:

1. How can you graphically represent the solution to this system of equations?
2. What method can be used to solve a system of equations if substitution isn't preferred?
3. What does it mean geometrically when two equations have a unique solution?
4. How would the solution change if the first equation were $x = 3y$ instead?
5. How can you verify the solution to this system of equations?

Tip: Always check your solutions by substituting the values back into both original equations.