August 2022
Intermediate to advanced
640 pages
15h 59m
English
Content preview from Algebra II All-in-One For Dummies
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Chapter 15
Solving Systems of Nonlinear Equations
IN THIS CHAPTER
Pinpointing solutions of parabola/line systems
Combining parabolas and circles to find intersections
Tackling polynomial, exponential, and rational systems
In systems of linear equations, the variables have exponents of 1 and you typically find only one solution (see Chapter 14). 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.
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, and you’ll be more convinced when your predictions come true. In this chapter, you find out at how many points a line and a parabola can cross and how many ways a parabola and a circle can cross. I also help you visualize a circle and an ellipse; when you put one on top of the other, you can plan on how many points of intersection you expect to find.
Crossing Parabolas ...
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.