Lesson Plan

Identify a linear-quadratic system (one linear equation and one quadratic equation in two variables) and explain why it can have 0, 1, or 2 solutions

Solve a linear-quadratic system algebraically using substitution: substitute the linear equation into the quadratic, solve the resulting one-variable quadratic, and back-substitute

Solve a linear-quadratic system graphically by identifying intersection points of the line and the parabola (or circle)

Interpret the solutions geometrically: 0 solutions means no intersection, 1 solution means tangency, 2 solutions means two intersection points

Verify algebraic solutions by checking both coordinates in both original equations

HSA.REI.C.7