Q1
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 :
Answer: C
Key fact: two straight lines either meet at exactly one point, are parallel (never meet), or coincide (meet everywhere).
- (A) No solution means the lines never meet, so they are parallel. True.
- (B) Coincident lines share every point, so the system has infinitely many solutions, not a finite number. False.
- (C) Two distinct straight lines cannot meet at exactly two points. False.
- (D) Exactly one solution means the lines intersect at one point. True.
In terms of coefficients: a/d ≠ b/e gives intersecting lines; a/d = b/e ≠ c/f gives parallel lines; a/d = b/e = c/f gives coincident lines.
Answer: A and D only (option 3)