Introduction to Systems of Nonlinear Equations and Inequalities: Two Variables

Learning Objectives

By the end of this section, you will be able to:

  • Solve a system of nonlinear equations using substitution.
  • Solve a system of nonlinear equations using elimination.
  • Graph a nonlinear inequality.
  • Graph a system of nonlinear inequalities.

Halley’s Comet orbits the sun about once every 75 years. Its path can be considered to be a very elongated ellipse. Other comets follow similar paths in space. These orbital paths can be studied using systems of equations. These systems, however, are different from the ones we considered in the previous section because the equations are not linear.

A comet streaking across a starry sky.

Figure 1. Halley’s Comet (credit: “NASA Blueshift”/Flickr)

In this section, we will consider the intersection of a parabola and a line, a circle and a line, and a circle and an ellipse. The methods for solving systems of nonlinear equations are similar to those for linear equations.