https://file.aiquickdraw.com/mathbot/file/1730521745746zajukp4g.jpg

The image shows a system of equations:

\[
x = 2y
\]
\[
2x + 5y = 9
\]

To solve this system of equations, we can substitute the expression for \( x \) from the first equation into the second equation.

### Step-by-Step Solution:

1. **Substitute \( x = 2y \) into the second equation:**
   \[
   2(2y) + 5y = 9
   \]
   Simplify this:
   \[
   4y + 5y = 9
   \]
   \[
   9y = 9
   \]

2. **Solve for \( y \):**
   \[
   y = \frac{9}{9} = 1
   \]

3. **Substitute \( y = 1 \) back into the first equation to find \( x \):**
   \[
   x = 2(1) = 2
   \]

### Solution:
The solution to the system is:
\[
x = 2, \quad y = 1
\]

Would you like a further breakdown of any part of the process, or do you have additional questions?

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Here are 5 related questions to expand on this problem:
1. What would happen if the equations had no solution?
2. How do we identify if a system of equations is dependent (infinitely many solutions)?
3. How can we solve systems of equations using the elimination method?
4. Can systems of equations be solved graphically, and how?
5. What are some applications of systems of equations in real-life situations?

**Tip:** Always check your solution by substituting the values back into the original equations to ensure they satisfy both equations.

Solve the system of equations:
x = 2y
2x + 5y = 9

Learn how to solve a system of linear equations using the substitution method. This example walks through solving x = 2y and 2x + 5y = 9, covering essential algebraic concepts. Ideal for students in Grades 8-10.

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