Solve linear-quadratic systems

What you'll learn

1. 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
2. Solve a linear-quadratic system algebraically using substitution: substitute the linear equation into the quadratic, solve the resulting one-variable quadratic, and back-substitute
3. Solve a linear-quadratic system graphically by identifying intersection points of the line and the parabola (or circle)
4. Interpret the solutions geometrically: 0 solutions means no intersection, 1 solution means tangency, 2 solutions means two intersection points
5. Verify algebraic solutions by checking both coordinates in both original equations

Prerequisites

• Solve quadratic equations
• Solve systems of linear equations