Chapter 13

# Solving Systems of Nonlinear Equations and Inequalities

IN THIS CHAPTER Pinpointing solutions of parabola/line systems Combining parabolas and circles to find intersections Attacking polynomial, exponential, and rational systems Exploring the shady world of nonlinear inequalities

In systems of linear equations, the variables have exponents of 1, and you typically find only one solution (see Chapter 12). The possibilities for multiple solutions in systems seem to grow as the exponents of the equations get larger, creating systems of nonlinear equations. For example, a line and parabola may intersect in two points, at one point, or at no point at all. A circle and ellipse can intersect in four different points. And consider inequalities. The graphs of inequalities involve many solutions. When you put two inequalities together, the possibilities are infinitely exciting (well, at least from my perspective).

One of the most important parts of solving nonlinear systems is planning. If you have an inkling as to what’s coming, you’ll have an easy time planning for the solution, ...

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