If `(a_(1))/(a_(2)) = (b_(1))/(b_(2)) ne (c_(1))/(c_(2))`, then the pair of linear equations has

Options

A. one solution
B. two solutions
C. No solution
D. Infinitely many solutions

Answer

To solve the given problem, we need to analyze the conditions under which a pair of linear equations has a unique solution, no solution, or infinitely many solutions.

### Step-by-Step Solution:

1. **Understanding the Ratios**: We are given the condition \((a_1)/(a_2) = (b_1)/(b_2) \neq (c_1)/(c_2)\). This means that the ratios of the coefficients of \(x\) and \(y\) in both equations are equal, but the ratio of the constants is different.

2. **Identifying the Type of Lines**:
- If \(\frac{a_1}{a_2} = \frac{b_1}{b_2}\), it implies that the two lines represented by the equations are either parallel or coincident.
- If \(\frac{c_1}{c_2} \neq \frac{a_1}{a_2}\) (or \(\frac{b_1}{b_2}\)), it indicates that the lines are not coincident.

3. **Conclusion About the Lines**: Since the ratios of the coefficients of \(x\) and \(y\) are equal, but the ratio of the constants is not equal, the two lines must be parallel.

4. **Determining the Number of Solutions**: Parallel lines do not intersect, which means there is no solution to the system of equations.

### Final Answer:
The pair of linear equations has **no solution**.

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