Algebra › Section K · Conics › Topic K.5
Systems of nonlinear equations
A linear system's two lines cross once or never — a nonlinear system's curves can tango twice, four times, or not at all. The algebra is familiar: substitution and elimination, straight from the linear playbook. The difference is that quadratics answer with two roots, and every root must find its partner.
In this topic
- When a line meets a curve
- By graphing: see the intersections
- How many solutions should I expect?
- Substitution: the engine
- Worked example: pairing each root with its partner
- Worked example: elimination with four solutions
- Check every candidate, report every survivor
- Common mistakes to avoid
- Key takeaways
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