System of Linear Inequalities two or more linearinequalities in the same two variables.Solution of a system of linear inequalities Anordered pair that is a solution of each inequality in thesystem.Graph of a system of linear inequalities Thegraph of all solutions of the system.
Example 1: Graph a system of two linear inequalitiesGraph the system of inequalities. y > 5x - 2 Inequality 1 y ≤ 3x + 6 Inequality 2SOLUTIONStep 1 Graph each inequality.Step 2 Find the intersection of the half-planes.
Example 2: Multiple Choice PracticeWhich graph best represents the solution to thissystem of inequalities. y>3x+1 2x-4y>4SOLUTIONStep 1 Choose a pointthat lies in the shadedregion of each graph.Step 2 Test the point.
TRY ON YOUR OWNGraph the system of linear inequalities.1. 2x + y > -1 2. y≤ 2x y< 3x + 2 x≥ -2
Example 3: Graph a system of three linear inequalitiesGraph the system of inequalities. y ≥ -1 Inequality 1 x > -2 Inequality 2 x + 2y ≤ 4 Inequality 3SOLUTIONGraph all three inequalities in the same coordinate plane.
Example 4: Write a system of linear inequalitiesWrite a system of inequalities for the shaded region.SOLUTIONInequality 1Inequality 2The system of inequalities forthe shaded region is: