7.9 notes[1]

System of Linear Inequalities two or more linear inequalities in the same two variables.

Solution of a system of linear inequalities An ordered pair that is a solution of each inequality in the system.

Graph of a system of linear inequalities The graph of all solutions of the system.

Example 1: Graph a system of two linear inequalities

Graph the system of inequalities. y > 5x - 2 Inequality 1 y ≤ 3x + 6 Inequality 2

SOLUTION Step 1 Graph each inequality.

Step 2 Find the intersection of the half-planes.

Example 2: Multiple Choice PracticeWhich graph best represents the solution to this system of inequalities. y>3x+1 2x-4y>4

SOLUTIONStep 1 Choose a point that lies in the shaded region of each graph.

Step 2 Test the point.

TRY ON YOUR OWNTRY ON YOUR OWN

Graph the system of linear inequalities.Graph the system of linear inequalities.

1. 1. 2x + y > -1 2x + y > -1 2. 2. y≤ 2xy≤ 2x y< 3x + 2 x≥ -2y< 3x + 2 x≥ -2

Example 3: Graph a system of three linear inequalities

Graph 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 1 Inequality 2

The system of inequalities for the shaded region is:

HOMEWORK: Textbook p. 437 # 3-15 every 3rd