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?

Two linear equations are given:

$px + qy = r$

$mx + ny = s$

The question asks which statements about their graphical relationships are incorrect.

Two lines in a plane can relate in three ways:

Lines intersect at one point when they have different slopes. This gives exactly one solution.

Lines are parallel when they have the same slope but different intercepts. This gives no solutions.

Lines overlap when they are identical. This gives infinite solutions.

Statement (A) claims lines are intersecting if the system has only one solution.

This is correct. When two lines intersect at exactly one point, there is exactly one solution.

Statement (B) claims lines are overlapping if the system has a finite number of solutions.

This is incorrect. Overlapping lines are the same line, which means every point on the line satisfies both equations. This gives infinite solutions, not a finite number.

Statement (C) claims lines are parallel if the system has infinite solutions.

This is incorrect. Parallel lines never meet, giving zero solutions. Infinite solutions occur when lines overlap (are identical), not when they are parallel.

Statements (B) and (C) are incorrect.