The graphs of ax + by = c, dx+ey = f will be,
(A) Parallel if the system has no solution.
(B) Coincident if the system has finite number of solutions.
(C) Intersecting if the system has two solutions
(D) Intersecting if the system has only one solution
Choose the correct answer from the options given below :

(A) Parallel if the system has no solution: True. If the two lines are parallel, they do not intersect, implying the system of equations has no solution. This occurs when the slopes of the lines are equal but their intercepts differ.

(D) Intersecting if the system has only one solution: True. If the lines intersect at exactly one point, the system has a unique solution. This happens when the lines have different slopes.

(B) Coincident if the system has a finite number of solutions: Incorrect. If the lines are coincident, the system has infinitely many solutions, not a finite number.

(C) Intersecting if the system has two solutions: Incorrect. Two linear equations can intersect at only one point, meaning the system cannot have two solutions.

 The nature of the solutions depends on how the lines relate geometrically:

Parallel lines → No solution (A is correct).

Intersecting lines → Unique solution (D is correct).

Lines cannot intersect at more than one point, ruling out C, and coincident lines lead to infinitely many solutions, ruling out B.

Therefore, the correct answer is option C.