We are given the following system of linear equations:

\[
\frac{x}{11} - \frac{y}{8} = -2 \tag{1}
\]
\[
\frac{x}{2} - \frac{y}{4} = 3 \tag{2}
\]

We can solve this system using substitution or elimination. Let's proceed step by step using the elimination method to simplify the equations.

### Step 1: Eliminate the fractions
To make the equations easier to handle, we multiply each equation by the least common multiple (LCM) of the denominators.

- For equation (1), multiply by 88 (LCM of 11 and 8):
  \[
  88 \times \left( \frac{x}{11} - \frac{y}{8} \right) = 88 \times -2
  \]
  \[
  8x - 11y = -176 \tag{3}
  \]

- For equation (2), multiply by 4 (LCM of 2 and 4):
  \[
  4 \times \left( \frac{x}{2} - \frac{y}{4} \right) = 4 \times 3
  \]
  \[
  2x - y = 12 \tag{4}
  \]

### Step 2: Use elimination
We now have the following system:

\[
8x - 11y = -176 \tag{3}
\]
\[
2x - y = 12 \tag{4}
\]

We will eliminate one variable by multiplying equation (4) by 11 to align the coefficients of \(y\):

\[
11 \times (2x - y) = 11 \times 12
\]
\[
22x - 11y = 132 \tag{5}
\]

### Step 3: Subtract the equations
Now subtract equation (3) from equation (5):

\[
(22x - 11y) - (8x - 11y) = 132 - (-176)
\]
\[
22x - 8x = 132 + 176
\]
\[
14x = 308
\]
\[
x = \frac{308}{14} = 22
\]

### Step 4: Substitute \(x = 22\) into equation (4)
Now that we know \(x = 22\), substitute it into equation (4):

\[
2(22) - y = 12
\]
\[
44 - y = 12
\]
\[
y = 44 - 12 = 32
\]

### Final Solution:
The solution to the system of equations is:
\[
x = 22, \quad y = 32
\]

Would you like more details or have any questions? Here are some related problems you can try:

1. Solve the system: \(\frac{x}{5} - \frac{y}{3} = 7\) and \(\frac{x}{2} + \frac{y}{4} = 1\).
2. Solve the system: \(3x - 4y = 9\) and \(5x + 2y = 7\).
3. Solve the system using substitution: \(x + 2y = 10\) and \(3x - y = 5\).
4. Solve the system: \(\frac{2x}{3} + \frac{y}{6} = 5\) and \(\frac{x}{4} - \frac{y}{3} = 2\).
5. Find the solution of \(x - 4y = -1\) and \(2x + 3y = 12\).

**Tip:** When dealing with fractions in systems of equations, multiplying through by the LCM of the denominators can help simplify the process.

Explore a step-by-step solution to solve the system of linear equations X/11 - Y/8 = -2 and X/2 - Y/4 = 3 using the elimination method. This problem covers key algebraic concepts like fractions and linear equations, suitable for students in Grades 9-11.

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