NY Next Generation Math AII-A.REI.7.b

MathGrades 9–12Solve systems of equations.

The Standard

Solve a system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

New York State Next Generation Mathematics Learning Standards

Teacher's field guide

What Students Need to Do: Students solve Algebra II systems containing one linear and one quadratic equation, limited to parabolas and circles. They use algebraic and graphical methods to find common ordered pairs.
What Mastery Looks Like: The student substitutes or eliminates accurately, finds every intersection, and verifies each point in both equations. A graph confirms the number and approximate locations of solutions.
Common Misconceptions: Students may find x-values without corresponding y-values, lose a solution after taking square roots, or assume every system has two intersections. They may extend the conic scope beyond parabolas and circles.
How to Assess It: Ask students to solve y equals x plus 1 with x squared plus y squared equals 25 algebraically and graphically, then verify all intersection points.

Lesson moves

Overlay line, parabola, and circle transparencies to predict intersection counts before solving.
Ask students how the graph can reveal whether an algebraic solution set is incomplete.
Play system-method match with line-parabola and line-circle systems suited to substitution or elimination.
Model where a straight path intersects a circular boundary or parabolic arch.

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