`{:(kx + 2y = 5),(3x + y = 1):}` Find the value of `k` for which given lines are not parallel to each other.

Answer

To find the value of `k` for which the given lines are not parallel to each other, we need to analyze the equations of the lines and apply the condition for non-parallel lines.

### Step-by-Step Solution:

1. **Write the equations in standard form:**
The given equations are:
- \( kx + 2y = 5 \) (Equation 1)
- \( 3x + y = 1 \) (Equation 2)

2. **Rewrite the equations:**
We can rewrite these equations in the form \( Ax + By + C = 0 \):
- For Equation 1: \( kx + 2y - 5 = 0 \)
- For Equation 2: \( 3x + y - 1 = 0 \)

3. **Identify coefficients:**
From the equations, we can identify:
- For Equation 1: \( A_1 = k, B_1 = 2, C_1 = -5 \)
- For Equation 2: \( A_2 = 3, B_2 = 1, C_2 = -1 \)

4. **Apply the condition for non-parallel lines:**
Two lines are not parallel if the ratio of their coefficients of \( x \) and \( y \) are not equal:
\[ \frac{A_1}{A_2} \neq \frac{B_1}{B_2} \]
Substituting the values:
\[ \frac{k}{3} \neq \frac{2}{1} \]

5. **Cross-multiply to solve for k:**
Cross-multiplying gives:
\[ k \cdot 1 \neq 2 \cdot 3 \]
Simplifying this, we find:
\[ k \neq 6 \]

### Conclusion:
The value of \( k \) for which the given lines are not parallel to each other is any value except \( k = 6 \).