System of nonlinear inequalities

Definition

A system of nonlinear inequalities consists of multiple inequalities involving nonlinear expressions. The solution is the set of points that satisfy all inequalities simultaneously.

5 Must Know Facts For Your Next Test

1. Nonlinear inequalities can involve quadratic, cubic, or higher-degree polynomials, as well as rational and radical expressions.
2. The solution to a system of nonlinear inequalities is typically a region in the plane rather than a single point.
3. Graphing each inequality separately and finding their intersection helps visualize the solution set.
4. Boundary lines or curves are often included in the solution if the inequality is non-strict (e.g., $\leq$ or $\geq$).
5. Test points can be used to determine which regions satisfy each inequality.

Review Questions

• How do you graphically represent the solution to a system of nonlinear inequalities?
• What steps are involved in solving a system of nonlinear inequalities?
• How does one determine whether boundary lines or curves are part of the solution set?

Related terms

Nonlinear Equation: An equation involving variables raised to powers other than one or involving products of variables.

Inequality: A mathematical statement that indicates one quantity is larger or smaller than another, using symbols like $<$, $>$, $\leq$, and $\geq$.

Feasible Region: The set of all possible points that satisfy a given system of inequalities.