The values of p, for which the equations `6x + py - 5 = 0 and 3x + 2y - 8 = 0` have unique solution is :

Options

A. `p = 4`
B. `p != 4`
C. `p = -4`
D. `p != -4`

Answer

To determine the values of \( p \) for which the equations \( 6x + py - 5 = 0 \) and \( 3x + 2y - 8 = 0 \) have a unique solution, we can use the condition for unique solutions of a system of linear equations.

### Step-by-step Solution:

1. **Identify the coefficients**:
For the first equation \( 6x + py - 5 = 0 \), we have:
- \( a_1 = 6 \)
- \( b_1 = p \)
- \( c_1 = -5 \)

For the second equation \( 3x + 2y - 8 = 0 \), we have:
- \( a_2 = 3 \)
- \( b_2 = 2 \)
- \( c_2 = -8 \)

2. **Apply the condition for unique solutions**:
The condition for the system of equations to have a unique solution is that the ratio of the coefficients of \( x \) and \( y \) must not be equal. This can be expressed as:
\[ \frac{a_1}{a_2} \neq \frac{b_1}{b_2} \]

3. **Substitute the values**:
Substituting the coefficients into the inequality:
\[ \frac{6}{3} \neq \frac{p}{2} \]

4. **Simplify the left side**:
Simplifying \( \frac{6}{3} \) gives:
\[ 2 \neq \frac{p}{2} \]

5. **Cross-multiply to eliminate the fraction**:
Cross-multiplying gives:
\[ 2 \cdot 2 \neq p \]
which simplifies to:
\[ 4 \neq p \]

6. **Conclusion**:
Thus, the values of \( p \) for which the equations have a unique solution are:
\[ p \neq 4 \]

### Final Answer:
The values of \( p \) for which the equations have a unique solution are \( p \neq 4 \).