Nonlinear systems and intersections

Explore nonlinear systems of equations by connecting algebraic solutions with intersection points. This precalculus set develops substitution and elimination through line–parabola, line–circle, circle–circle and rational systems. Conceptual and multiselect questions check tangency, coincident curves, domain exclusions and the completeness of a solution set. Worked explanations include substitution checks and distinguish a candidate root from a valid ordered pair. Difficulty grows from direct verification to parameter conditions and error analysis; no calculus is required.