Systems of Linear Inequalities
Onelinear inequalityin two variables divides the plane into twohalf-planes. To graph the inequality, graph the equation of the boundary. Use a solid line if the symboloris used because the boundary is included in the solution. Use a dashed line ifis used to indicate that the boundary is not part of the solution. Shade the appropriate region. Unless you are graphing a vertical line the sign of the inequality will let you know which half-plane to shade. If the symboloris used, shade above the line. If the symboloris used shade below the line. For a vertical line, larger solutions are to the right and smaller solutions are to the left. Asystemof two or more linear inequalities can divide the plane into more complex shapes.
Example 1:
Graph
Example 2:
Graph the system of linear inequalities.
Graphing the three lines and shading the region enclosed, we get the figure below.