Solve Linear and Quadratic Systems Algebraically Remember solving SYSTEMS of LINEAR equations . . . you could do it graphically, or algebraically using substitution or elimination (A.K.A. linear combinations). Try this: Consider the linear system: y = 2x + 5 x + 2y = 15 . Solve the linear system using substitution. b. Explain what that ordered pair represents. SUBSTITUTION was used because it is the only method we can use to solve linear-quadratic systems algebraically. Because we are dealing with quadratic equations, it is natural to expect more than one answer. Think about this: Consider the sketch of a line and a parabola. a. What is the maximum number of intersection points that a line and a parabola could have? Illustrate with a picture. b. What is the minimum number of intersection points c. Is it possible for a line and a parabola to intersect in only one point? If so, illustrate with a picture.

1. 3. 2. 4. Use a graphing calculator to solve the system below. Use the “Calculate Intersection” and “Table” features. Find a good window where you can see both equations and their intersection points clearly. Draw a picture of your screen and state the window you used. y = x2 + 2x – 6 3x + y = -12 Xmin= Xmax= Xscl= Ymin= Ymax= Yscl=