Unique, none or infinitely many solutions of a 2×2 linear system

CAT has tested this idea 3 times across 3 papers, from 2020 to 2024. Solve one, and the others are the same method with different numbers or wording, which is why repeated concepts are the most efficient thing to practise.

Question	What it asks	Answer
CAT 2024 Slot 3 · QA Q2	necessary condition for no solution	A
CAT 2023 Slot 3 · QA Q3	infinitely many solutions; maximise ab	B
CAT 2020 Slot 3 · QA Q15	unique solution iff \|k\| ≠ 2	C

Part of Equations (52 questions since 2017).