If `ax+by=c` and `lx+my=n` has unique solution then the relation between the coefficients will be of the form:

Options

A. `amnelb`
B. `am=lb`
C. `ab=lm`
D. `abnelm`

Answer

To determine the relation between the coefficients of the equations \( ax + by = c \) and \( lx + my = n \) for them to have a unique solution, we can follow these steps:

### Step-by-step Solution:

1. **Identify the equations**:
We have two equations:
\[ ax + by = c \quad \text{(1)} \]
\[ lx + my = n \quad \text{(2)} \]

2. **Rewrite the equations in standard form**:
We can rewrite both equations in the standard form \( A_1x + B_1y + C_1 = 0 \) and \( A_2x + B_2y + C_2 = 0 \):
\[ ax + by - c = 0 \quad \text{(1')} \]
\[ lx + my - n = 0 \quad \text{(2')} \]

3. **Identify coefficients**:
From the rewritten equations, we can identify the coefficients:
- For equation (1'): \( A_1 = a, B_1 = b, C_1 = -c \)
- For equation (2'): \( A_2 = l, B_2 = m, C_2 = -n \)

4. **Condition for unique solution**:
For the system of equations to have a unique solution, the following condition must hold:
\[ \frac{A_1}{A_2} \neq \frac{B_1}{B_2} \]

5. **Substituting coefficients**:
Substituting the coefficients we identified:
\[ \frac{a}{l} \neq \frac{b}{m} \]

6. **Cross-multiplying**:
Cross-multiplying gives:
\[ am \neq bl \]

### Final Answer:
Thus, the relation between the coefficients for the equations \( ax + by = c \) and \( lx + my = n \) to have a unique solution is:
\[ am \neq bl \]