Question

If \(\frac {a_1}{a_2}=\frac {b_1}{b_2}≠\frac {c_1}{c_2}\), then the lines are

• A. Unique solution
• B. Coincident
• C. Infinitely many solutions
• D. No solutions

Answer 1

The Correct Option is D

To solve the problem, we analyze the relationship between two linear equations based on their coefficients.

1. General Form of a Pair of Linear Equations:
Consider two linear equations in the form:
$ a_1x + b_1y + c_1 = 0 $
$ a_2x + b_2y + c_2 = 0 $

2. Condition Given:
It is given that:
$ \frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2} $

3. Interpretation of the Condition:
This means that the two lines have the same slope (they are parallel), but different intercepts.
Therefore, the lines are parallel and **distinct**.

4. Geometrical Implication:
Since the lines are parallel but not the same, they will never intersect.
Thus, the system of equations has no solution.

Final Answer:
The lines are such that there are $ {\text{No solutions}} $