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Linear Inequalities in Two Variables
Chapter 4 Section 4 Linear Inequalities in Two Variables
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Linear Inequality in Two Variables
Ax + By = C Straight lines when graphed. Replace the = symbol with an inequality Linear Inequality in Two Variables
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Examples x + y > 2 5y ≤ 15 2x – y > 4
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Solution of an inequality
Two variables Ordered pair of real number that satisfy the inequality Graph Region, half plane Solid line: line is part of the graph Dashed line: not part of the graph
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Solve Replace the inequality symbol with = Graph the line
Choose a test point. True statement, shade that part of the half plane that contains the test point.
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Practice Solve and graph the solution set 2x – 3y < 6
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Graph the solution set 2x + y > 6 x ≤ - 4
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System of Linear Inequalities
Two or more linear inequalities Solution Ordered pair that satisfies each inequality in the system
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Graph the solution Solution Replace the inequality with =
Graph each line Lines intersect, so pick a test point in each region.
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One more Graph the solution set
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Graph the Solution set c) d)
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