Solutions to a system of linear inequalities is the intersection of each of the corresponding half planes.

• See how the solution to a system of linear inequalities is the intersection of each of the corresponding half planes
• See how the test point is used to verify the solution set
• Understand that the solution regions can be one of four regions or no solution at all
• Understand that the graph of a system of inequalities may or may not include parts of the boundaries as part of the solution

• solution set
• boundary lines
• half plane
• linear inequality

Begin by reviewing a graph of one linear inequality by testing a point and trying different shaded regions including solid or dotted boundary lines. Then change the inequalities to get a particular region as the solution set to the system. This is followed up by testing a point algebraically. Continue to look at other possible systems, including a system with a horizontal line and also a system with parallel lines. Finally, find the inequalities to have a particular solution set. This is followed by testing a point algebraically.