`11x-24y=8`
`kx-36y=5`
In the system of equations above, k is a constant. If the system has no solutions, what is the value of k?

Explanation

To solve the problem, we need to determine the value of \( k \) such that the system of equations has no solutions. This occurs when the lines represented by the equations are parallel, which means they have the same slope but different y-intercepts.

### Step-by-step Solution:

1. **Identify the equations**:
The given equations are:
\[ 11x - 24y = 8 \quad \text{(1)} \]
\[ kx - 36y = 5 \quad \text{(2)} \]

2. **Convert both equations to slope-intercept form (y = mx + b)**:
For equation (1):
\[ 11x - 24y = 8 \]
Rearranging gives:
\[ -24y = -11x + 8 \]
Dividing by -24:
\[ y = \frac{11}{24}x - \frac{8}{24} \]
Thus, the slope \( m_1 \) of the first equation is \( \frac{11}{24} \).

For equation (2):
\[ kx - 36y = 5 \]
Rearranging gives:
\[ -36y = -kx + 5 \]
Dividing by -36:
\[ y = \frac{k}{36}x - \frac{5}{36} \]
Thus, the slope \( m_2 \) of the second equation is \( \frac{k}{36} \).

3. **Set the slopes equal for parallel lines**:
Since the lines are parallel, we set the slopes equal to each other:
\[ \frac{11}{24} = \frac{k}{36} \]

4. **Cross-multiply to solve for \( k \)**:
Cross-multiplying gives:
\[ 11 \cdot 36 = 24 \cdot k \]
Simplifying this:
\[ 396 = 24k \]

5. **Solve for \( k \)**:
Dividing both sides by 24:
\[ k = \frac{396}{24} \]
Simplifying further:
\[ k = 16.5 \quad \text{or} \quad k = \frac{33}{2} \]

### Final Answer:
The value of \( k \) such that the system of equations has no solutions is:
\[ \boxed{16.5} \quad \text{or} \quad \frac{33}{2} \]