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To solve this system of equations, we can use either the elimination or substitution method. Here’s the system:

1. \( 2x - 3y = 12 \)
2. \( 4x + 3y = 24 \)

### Step-by-Step Solution using Elimination Method:

1. **Add the equations together to eliminate \( y \):**

   \[
   (2x - 3y) + (4x + 3y) = 12 + 24
   \]

   Simplifying:

   \[
   6x = 36
   \]

2. **Solve for \( x \):**

   \[
   x = \frac{36}{6} = 6
   \]

3. **Substitute \( x = 6 \) into one of the original equations to find \( y \):**

   Using the first equation, \( 2x - 3y = 12 \):

   \[
   2(6) - 3y = 12
   \]

   \[
   12 - 3y = 12
   \]

   Subtract 12 from both sides:

   \[
   -3y = 0
   \]

   \[
   y = 0
   \]

### Solution:
The solution to the system is:
\[
x = 6, \quad y = 0
\]

Would you like further details or have any questions?

Here are some related questions to expand your understanding:

1. What would happen if you solved the system using the substitution method?
2. How can you check if a solution to a system of equations is correct?
3. What does it mean if a system of equations has no solutions?
4. How would you solve the system if both equations had different coefficients for \( y \)?
5. What are the differences between dependent, independent, and inconsistent systems?

**Tip:** When using elimination, try to align terms so one variable cancels out easily.

Solve the system of equations: 2x - 3y = 12 and 4x + 3y = 24.

Learn how to solve the system of linear equations 2x - 3y = 12 and 4x + 3y = 24 using the elimination method. This solution provides a step-by-step approach suitable for students in Grades 8-10, covering key algebraic concepts.

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