The correct answer is Option (3) → (B) and (C) only
Analysis of the Statements
- (A) Intersecting, if the system has only one solution: This is correct. When two lines have different slopes, they cross at exactly one point. This point represents the unique solution $(x, y)$ that satisfies both equations.
- (B) Overlapping, if the system has a finite number of solutions: This is incorrect. If lines overlap (coincide), every point on one line is also on the other. This results in an infinite number of solutions. In a system of linear equations, you can have zero solutions, one solution, or infinite solutions—you can never have a "finite" number like two or three.
- (C) Parallel, if the system has infinite solutions: This is incorrect. If two lines are parallel, they never meet. Because they have no points in common, the system has no solution. Parallel lines only have infinite solutions if they are the same line (overlapping), but the term "parallel" in geometry usually implies they are distinct with no intersection.
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