Graphing Systems of Linear Inequalities in Two Variables

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Linear Inequalities in 2 Variables

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Presentation transcript:

Graphing Systems of Linear Inequalities in Two Variables Section 3.1 Graphing Systems of Linear Inequalities in Two Variables

Graphing Linear Inequalities Ex. Graph Notice that the line (=) is part of the solution Also, any point in the lower half-plane satisfies the inequality so this region is shaded.

Graphing Linear Inequalities Ex. Graph The line (=) is not part of the solution (so it is dashed. Any point in the lower half-plane satisfies the inequality.

Procedure for Graphing Linear Inequalities Draw the graph of the equation obtained by replacing the inequality symbol with an equal sign. Make the line dashed if the inequality symbol is < or >, otherwise make it solid. Pick a test point in one of the half planes, substitute the x and y values into the inequality (use the origin whenever possible). If the inequality is satisfied, shade the half plane containing the test point otherwise shade the other half plane.

True so shade region containing (0,0) Ex. Graph Dashed since < Test (0,0): 3(0)+2(0) < 6 True so shade region containing (0,0)

Ex. Graph Ex. Graph

Ex. Graph the solution set for the system: Points must satisfy both inequalities (overlap of individual shaded regions)

Unbounded Region Bounded Region