A student writes only (1) solution for (3x+2y=12) and (6x+4y=24). What is the mistake?

Correct answer: Treating coincident lines as having one solution

The direct answer is B: treating coincident lines as having one solution. The second equation is exactly twice the first: 2(3x+2y=12) gives 6x+4y=24. Therefore both equations represent the same line, not two different lines. Every point on this common line satisfies both equations, so the pair has infinitely many solutions. A is wrong because the lines are not distinct parallel lines; distinct parallel lines have no solution, while coincident lines overlap. B correctly identifies the student’s mistake: a coincident pair was incorrectly assigned one solution. C is wrong because intersecting lines normally have exactly one solution, so calling them inconsistent is incorrect. D is irrelevant and false; reversing axis names is not the issue and would not explain the number of solutions. A useful check is to compare all ratios: 6/3=2, 4/2=2, and 24/12=2. Equal ratios indicate coincident lines. Memory cue: one intersection means one solution; complete overlap means infinitely many.