Recall that when the inequality is greater than, y > a, y > a, or less than, y < a, y < a, the graph is drawn with a dashed line.
Graphing a nonlinear inequality is much like graphing a linear inequality. A nonlinear inequality is an inequality containing a nonlinear expression. Now, we will follow similar steps to graph a nonlinear inequality so that we can learn to solve systems of nonlinear inequalities. We have already learned to graph linear inequalities by graphing the corresponding equation, and then shading the region represented by the inequality symbol. There are three possible types of solutions for a system of nonlinear equations involving a parabola and a line.Ĥ x 2 + y 2 = 13 x 2 + y 2 = 10 4 x 2 + y 2 = 13 x 2 + y 2 = 10 Graphing a Nonlinear InequalityĪll of the equations in the systems that we have encountered so far have involved equalities, but we may also encounter systems that involve inequalities. There is, however, a variation in the possible outcomes. We solve one equation for one variable and then substitute the result into the second equation to solve for another variable, and so on. The substitution method we used for linear systems is the same method we will use for nonlinear systems. Any equation that cannot be written in this form in nonlinear. Recall that a linear equation can take the form A x + B y + C = 0.
Solving a System of Nonlinear Equations Using SubstitutionĪ system of nonlinear equations is a system of two or more equations in two or more variables containing at least one equation that is not linear. The methods for solving systems of nonlinear equations are similar to those for linear equations. 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. Figure 1 Halley’s Comet (credit: "NASA Blueshift"/Flickr)
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