# 3.10 – Nonlinear Systems of Inequalities

## Objectives

• Define nonlinear system of inequalities.
• Identify points that satisfy a nonlinear inequality.
• Match a nonlinear inequality with the graph that represents it.
• List the steps in the process of graphing a nonlinear inequality.
• Solve a nonlinear system of inequalities.

## Key Terms

• Boundary Line – A solid or dashed line on a grpah that provides a border for the solution set.
• Solid: equal to (included in the solution)
• Dashed: not equal to (electric fence, do not cross, not included in the solution)
• Nonlinear Inequalities – Inequalities that are not straight (linear).
• Ex. Quadratic equations are nonlinear (they are parabolas)

## Notes

Graphing Inequalities
• The graph of this inequality is divided into two regions:
• Shaded: Shows all the points that are solutions
• Unshaded: Shows all the points that are not solutions

• How to Graph a Nonlinear Inequality
• Step 1: Change the inequality sign to an equal sign.
• Step 2: Graph the equation. Use dashed for < or >. Use solid for ≤ or ≥.
• Step 3: Choose a point (x,y) on either the inside or the outside the graph.
• Step 4: Substitute the point into the inequality and determine if that point makes the inequality true or false.