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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.
    • Step 5: Shade
      • If true, shade the region that contains that point.
      • If false, shade the region that does not contain the point.
Alg2A-03.10-Nonlinear-Graphs Ex
Alg2A 03.10 - Nonlinear Graphs 02
Examples
  • Example 1: Nonlinear Inequality System
    • The region containing all the solutions for the circle inequality is blue.
    • The regions containing all the solutions for the hyperbola inequality are pink.
    • The regions containing all the solutions for the system of inequalities are purple.
    • Every point inside the two purple regions makes both inequalities true.

 

Alg2A 03.10 - Nonlinear System Inequality

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