Simultaneous Equations — Practice Companion

Eight questions, building from straightforward to exam-style. Each one comes with a four-tier support ladder — use it in order, and only as far as you need:

🤔 Socratic prompt asks you a question to get you thinking · 💡 Hint gives you a piece of method · ✅ Check my answer tells you if you're right and nudges you if not · 👀 Worked solution is the last resort, and unlocks once you've genuinely tried. The aim isn't to avoid the ladder — it's to climb only as high as you need, and to notice where you needed it.

💛 Before you finish — a reflection

Look back over the eight questions and notice, without judgement:

Which case felt more secure — linear-linear or linear-quadratic? Starting from your stronger case is a sensible strategy when you're tired.
On the questions where you used the discriminant, did "how many roots" and "how many intersection points" feel like the same question yet? If not, that's the connection worth revisiting.
Where did you reach for the ladder, and which rung actually helped? A Socratic nudge, a hint, or checking-and-revising? Knowing which kind of help unsticks you is a tool for every future topic.

There's no score that matters here more than that last noticing.