The graphs of \(px + qy = r, mx + ny = s\) will be
(A) intersecting, if the system has only one solution.
(B) overlapping, if the system has a finite number of solutions.
(C) parallel, if the system has infinite solutions
Which of the statements below is/are incorrect?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (B) and (C) only
Each solution of a pair of linear equations is a point common to both lines, so the graphs show the number of solutions:
Intersecting lines — one common point, so one solution only
Coincident (overlapping) lines — every point is common, so infinitely many solutions
Parallel lines — no common point, so no solution
The question asks for the incorrect statements.
(A) intersecting, if the system has only one solution. Correct statement. Two lines that cross meet at one point only, which is the one solution.
(B) overlapping, if the system has a finite number of solutions. Incorrect statement. Overlapping lines share every point, so the system has infinitely many solutions, not a finite number.
(C) parallel, if the system has infinite solutions Incorrect statement. Parallel lines never meet, so the system has no solution; infinitely many solutions mean the lines overlap.