Find the value(s) of p for the following pair of equations:
`-x+ py =1 and px- y=1`, if the pair of equations has no solution.

Answer

To find the value(s) of \( p \) for which the pair of equations has no solution, we need to analyze the given equations:

1. **Equations**:
\[ -x + py = 1 \quad \text{(1)} \]
\[ px - y = 1 \quad \text{(2)} \]

2. **Identifying coefficients**:
From the first equation (1), we can identify:
- \( a_1 = -1 \)
- \( b_1 = p \)
- \( c_1 = -1 \) (after moving 1 to the left side)

From the second equation (2), we can identify:
- \( a_2 = p \)
- \( b_2 = -1 \)
- \( c_2 = -1 \) (after moving 1 to the left side)

3. **Condition for no solution**:
The condition for the pair of equations to have no solution (i.e., the lines are parallel) is given by:
\[ \frac{a_1}{a_2} = \frac{b_1}{b_2} \quad \text{and} \quad \frac{a_1}{a_2} \neq \frac{c_1}{c_2} \]

4. **Setting up the equations**:
Using the coefficients we identified:
\[ \frac{-1}{p} = \frac{p}{-1} \]

5. **Cross-multiplying**:
Cross-multiplying gives us:
\[ -1 \cdot -1 = p \cdot p \]
This simplifies to:
\[ 1 = p^2 \]

6. **Finding values of \( p \)**:
Taking the square root of both sides, we get:
\[ p = 1 \quad \text{or} \quad p = -1 \]

7. **Checking for parallel lines**:
We need to check which of these values satisfies the condition of parallel lines:
- For \( p = 1 \):
\[ \frac{-1}{1} = \frac{1}{-1} \quad \text{and} \quad \frac{-1}{1} \neq \frac{-1}{-1} \]
This holds true.
- For \( p = -1 \):
\[ \frac{-1}{-1} = \frac{-1}{-1} \quad \text{and} \quad \frac{-1}{-1} = \frac{-1}{-1} \]
This does not satisfy the condition since both ratios are equal.

8. **Conclusion**:
Therefore, the only value of \( p \) for which the pair of equations has no solution is:
\[ \boxed{1} \]