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## Linear Inequalities in Two Variables

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**Linear Inequalities in Two Variables**AII, 2.0: Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices.**Linear Inequalities in Two Variables**Objectives Key Words Linear inequality in two variables Boundary Line Dashed Shaded Half-Plane Test a point • Solve and graph linear inequalities in one variables • Solve and graph linear inequalities in two variables**Pre-requisite Check**Name the Symbol Check Solutions of Inequalities Check whether the given ordered pair is a solution of . True or False. • < • > • ≤ • ≥**Graph linear inequalities in one or two variables**• GRAPH the boundary line of the inequality. Use a dashed line for < or >. Use a solid line for ≤ or ≥. • TEST a point that is not on the boundary line to see whether it is a solution of the inequality. Then shade the appropriate half-plane Steps for graphing a linear inequality.**Example 1**y = < < – – y y 2. 2 SOLUTION – 2. a. Graph the boundary line Use a dashed line because 3 x ≤ Test the point (0, 0). It is not a solution, so shade the half-plane that does not contain (0, 0). Graph Linear Inequalities in One Variable Graph (a) and (b) in a coordinate plane.**Example 1**Test the point (0, 0). It is a solution, so shade the half-plane that contains (0, 0). 3. x ≤ x = 3. Graph Linear Inequalities in One Variable b. Graph the boundary line Use a solid line because**Checkpoint**x ANSWER – 1 > 2. y 1 ANSWER ≥ Graph Linear Inequalities in One Variable Graph the inequality in a coordinate plane. 1.**Checkpoint**ANSWER – 3 4. ANSWER < x 4 y ≤ Graph Linear Inequalities in One Variable Graph the inequality in a coordinate plane. 3.**Example 2**< < y y 2x 2x. 8 3x 2y ≥ – SOLUTION y = 2x. a. Graph the boundary line Use a dashed line because Graph Linear Inequalities in Two Variables Graph (a) and (b) in a coordinate plane. Test the point (1, 1). Because (1, 1)is a solution, shade the half-plane that contains (1, 1).**Example 2**b. Graph the boundary line . Use a solid line because 8. 3x 2y ≥ – Test the point . Because is not a solution, shade the half-plane that does not contain . ( ( ( ) ) ) 0, 0 0, 0 0, 0 8 3x 2y = – Graph Linear Inequalities in Two Variables**Checkpoint**y x ≥ ANSWER 6. ANSWER x – 3y 1 > Graph Linear Inequalities in Two Variables Graph the inequality in a coordinate plane. 5.**Conclusions**Summary Assignment If not completed in class, it will be due the following day we meet. Pg 182 (18, 26, 36, 44, 47) • What does a dashed boundary line on the graph of an inequality represent? • A dashed boundary line means that the points on that line are not solutions of the inequality.