The graphs of $+by = c$ and $dx+ey = f$ will be:

(A) parallel, if the system has no solution.
(B) coincident, if the system has finite numbers of solutions.
(C) intersecting, if the system has only one solution.

Which of the above statements is/are correct?

Choose the correct answer from the options given below:

(C) and (A) only

The correct answer is Option (3) → (C) and (A) only

Equations:

1. $ax + by = c$
2. $dx + ey = f$

Statement (A): Parallel lines → No solution

• Two lines are parallel if their slopes are equal:

$\frac{a}{b} = \frac{d}{e} \quad \text{but} \quad \frac{a}{b} \ne \frac{c}{f}$

• In this case, the lines never meet → no solution.

Statement (A) is correct.

Statement (B): Coincident lines → Finite number of solutions

• Coincident lines are identical, i.e., all points are solutions.
• Infinite solutions, not finite.

Statement (B) is incorrect.

Statement (C): Intersecting lines → One solution

• If the lines are not parallel and not coincident, they intersect at one point → one solution

Statement (C) is correct.

Correct answer: (C) and (A) only