Question

Two lines are given by the equations $ax + by = c$ and $dx + ey = f$. Do they intersect?
Statement A
A. $a, b, c, d, e, f$ are distinct \& real.
Statement B
B. $c \neq 0$ \& $f \neq 0$.

• A. The question can be answered by one of the statements alone but not by the other.
• B. The question can be answered by using either statement alone.
• C. The question can be answered by using both the statements together, but cannot be answered by using either statement alone.
• D. The question cannot be answered even by using both statements together.

Hint:

For two lines to intersect, they must be non-parallel: $\frac{a}{d} \neq \frac{b}{e}$.

Answer 1

The Correct Option is D

To determine intersection, we need to check if the lines are not parallel, i.e., $\frac{a}{d} \neq \frac{b}{e}$. Statement A tells only that the coefficients are distinct but doesn't guarantee $\frac{a}{d} \neq \frac{b}{e}$. Statement B tells nothing about slopes, only that constants are non-zero. Even together, they don’t confirm if lines are non-parallel.