1. 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.

2.
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
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