Linear Inequalities in Two Variables Chapter 4 Section 4 Linear Inequalities in Two Variables

Linear Inequality in Two Variables Ax + By = C Straight lines when graphed. Replace the = symbol with an inequality Linear Inequality in Two Variables

Examples x + y > 2 5y ≤ 15 2x – y > 4

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

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.

Practice Solve and graph the solution set 2x – 3y < 6

Graph the solution set 2x + y > 6 x ≤ - 4

System of Linear Inequalities Two or more linear inequalities Solution Ordered pair that satisfies each inequality in the system

Graph the solution Solution Replace the inequality with = Graph each line Lines intersect, so pick a test point in each region.

One more Graph the solution set

Graph the Solution set c) d)