Assess students' ability to solve systems involving a linear equation and a quadratic equation (and related cases) to find intersection points. Tasks should require applying algebraic methods (substitution, elimination), solving resulting quadratics, using the discriminant to determine the number and type of real solutions (two intersections, one tangent point, or none), verifying coordinates, and interpreting solutions in contextual word problems. Include problems that require sketching or reasoning about graphs to support algebraic answers.