3.3 Graph Systems of Linear Inequalities

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3.3 Graph Systems of Linear Inequalities

The following is a system of linear inequalities in two variables: Is (0,0) a solution for this system?? (3, -1) is a solution for this system. The graph of a system of linear inequalities is the graph of all solutions of the system. A solution of a system of linear inequalities is an ordered pair that is a solution of each inequality in the system.

Is (1,1) a solution to this system? No

Graph the system and locate all the solutions. Graph the line y = -3x -1 and “divide” the plane into 2 “half-planes”. (5,0) Test a point (like (5,0)) in one of the half planes to decide which half-plane to shade as solutions. This Region Graph the line y = x +2 (Make it “dashed”. (Why?) y=x+2 Test a point to decide which half-plane to shade. The set of all solutions is where the two half-planes intersect. y = -3x - 1

Is (3,2) a solution to this system? Yes

Graph this system of Three Inequalities. X=0 y=0 The Region where all three half-planes intersect, is the set of solutions.

Graph the system Name an ordered pair that is a solution to this system. Name an ordered pair that is NOT a solution to this system.