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 \( lx + my = n \) that ensures they have a unique solution, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the coefficients**:
From the equations:
- For the first equation \( ax + by = c \), the coefficients are:
- \( a_1 = a \)
- \( b_1 = b \)
- \( c_1 = c \)
- For the second equation \( lx + my = n \), the coefficients are:
- \( a_2 = l \)
- \( b_2 = m \)
- \( c_2 = n \)

2. **Condition for unique solutions**:
For the system of equations to have a unique solution, the following condition must hold:
\[ \frac{a_1}{a_2} \neq \frac{b_1}{b_2} \]
This means that the ratios of the coefficients of \( x \) and \( y \) must not be equal.

3. **Substitute the coefficients**:
Substitute the identified coefficients into the condition:
\[ \frac{a}{l} \neq \frac{b}{m} \]

4. **Cross-multiply to eliminate the fractions**:
To eliminate the fractions, we can cross-multiply:
\[ a \cdot m \neq b \cdot l \]

5. **Final relation**:
Thus, the relation between the coefficients that ensures a unique solution is:
\[ am \neq bl \]

### Conclusion:
The relation between the coefficients of the equations \( ax + by = c \) and \( lx + my = n \) for them to have a unique solution is:
\[ am \neq bl \]