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.