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The problem asks for the solution set of the following system of equations:

\[
\begin{cases}
\frac{x}{2} - \frac{y}{3} = 2 \\
\frac{x}{4} + \frac{y}{2} = 3
\end{cases}
\]

Let's solve this system step-by-step.

### Step 1: Solve the first equation
The first equation is:

\[
\frac{x}{2} - \frac{y}{3} = 2
\]

Multiply the entire equation by 6 to eliminate the denominators:

\[
6 \times \left(\frac{x}{2} - \frac{y}{3}\right) = 6 \times 2
\]

This simplifies to:

\[
3x - 2y = 12
\]

So, the first equation becomes:

\[
3x - 2y = 12 \quad (1)
\]

### Step 2: Solve the second equation
The second equation is:

\[
\frac{x}{4} + \frac{y}{2} = 3
\]

Multiply the entire equation by 4 to eliminate the denominators:

\[
4 \times \left(\frac{x}{4} + \frac{y}{2}\right) = 4 \times 3
\]

This simplifies to:

\[
x + 2y = 12
\]

So, the second equation becomes:

\[
x + 2y = 12 \quad (2)
\]

### Step 3: Solve the system
Now, we have the system:

\[
\begin{cases}
3x - 2y = 12 \\
x + 2y = 12
\end{cases}
\]

Add both equations to eliminate \(y\):

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

This simplifies to:

\[
4x = 24
\]

So,

\[
x = 6
\]

### Step 4: Substitute \(x = 6\) into the second equation
Substitute \(x = 6\) into equation (2):

\[
6 + 2y = 12
\]

This simplifies to:

\[
2y = 6 \quad \Rightarrow \quad y = 3
\]

### Solution
The solution set is:

\[
(x, y) = (6, 3)
\]

---

Do you have any questions, or would you like further details on any step?

Here are 5 related questions you can explore:
1. How can we solve systems of equations using substitution?
2. What is the method of elimination for solving linear systems?
3. How can you solve systems of equations with three variables?
4. What are consistent, inconsistent, and dependent systems?
5. How can matrices be used to solve systems of equations?

**Tip**: Multiplying both sides of an equation by a common denominator helps eliminate fractions and simplifies solving equations.

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

Learn how to solve a system of linear equations, x/2 - y/3 = 2 and x/4 + y/2 = 3, using the elimination method. This detailed solution demonstrates key algebraic concepts and is suitable for students in Grades 9-12.

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