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Chapter 12

Solving Systems of Nonlinear Equations and Inequalities

In This Chapter Figuring out where lines and parabolas meet Solving systems of equations involving circles and parabolas Finding where exponential equations intersect Solving systems of inequalities with graphs

The graphs of a line and a parabola may intersect in two points or one point or not at all. So, the solution of a system of equations involving both linear and quadratic equations, whose graphs are a line and a parabola, may have two solutions, one solution, or none at all. (Don’t you just love ambiguity?) The number of possible solutions increases with the powers on the variables of the equations.

In this chapter, you deal with the multiple solutions you find when working with systems that mix lines, parabolas, and circles. You also dabble with systems of inequalities to find a feasible region or area where all the points in the area are solutions of the system. Read on to find the methods to this madness.

Finding the Intersections of Lines and Parabolas

A line can cut through a parabola in two points, or ...

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