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:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (C) and (A) only
Equations:
- $ax + by = c$
- $dx + ey = f$
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