Section 11.4: Systems and Inequalities
Essential Ideas
  • A system of equations is two or more equations considered at the same time. The intersection point (or points) of the equations is called the simultaneous solution of a system of equations.

  • A system of linear inequalities is two or more inequalities with two first-degree variables considered at the same time. The intersection points (if any) of the inequalities is called the simultaneous solution of a system of inequalities.

  • Procedure for Graphing a Linear Inequality

    Step 1. Graph the boundary.
    Replace the inequality symbol with an equality symbol and draw the resulting line. This is the boundary line. Use a solid line when the boundary is included (< or >). Use a dashed line when the boundary is not included (< or>).

    Step 2. Test a point.
    Choose any point in the plane that is not on the boundary line; the point (0, 0) is usually the simplest choice. If this point, called a test point makes the inequality true, shade in that half-plane for the solution. If the test point makes the inequality false, shade in the other half-plane for the solution.