https://file.aiquickdraw.com/mathbot/file/1727364588641d0m7p406.jpg

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?

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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.

Solve the system of equations: x = 2y and -9x + 4y = 28.

Learn how to solve the system of linear equations x = 2y and -9x + 4y = 28 using the substitution method. This step-by-step solution is suitable for students in Grades 8-10, covering key algebraic concepts.

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