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Chapter 7 Section 6: Solving Systems of Linear Inequalities In this section, we will… Determine if a given ordered pair is a solution to a linear inequality or to a system of linear inequalities Solve a linear inequality Solve a system of linear inequalities Solve applications In chapter 2, we solved equations and inequalities in one-variable: equation: x2 inequalities: x2 x2 Now we will solve equations and inequalities in two-variables: equation: inequalities: y 13 x 2 y 13 x 2 y 13 x 2 Example: Determine if 2,0 is a solution of x 4 y 1 Example: Determine if 2, 14 is a solution of x 4 y 1 Example: A linear inequality has been graphed. Determine if the given points satisfy the inequality. 4,6 3,1 Example: A linear inequality has been graphed. Determine if the given points satisfy the inequality. 4, 6 3,1 Solving Linear Inequalities Graphically 1. Graph the boundary line. • Solve the inequality for y *** Remember to flip the sign if you multiply or divide both sides by a negative number *** • Graph using the slope and y-intercept • Solid line if or • Dashed line if < or > 2. Determine which side of the boundary line to shade. • Pick a test point that does not fall on the boundary line • True statement – shade that side • False statement – shade the other side Example: Solve the linear inequality by graphing. y 3x Example: Solve the linear inequality by graphing. 3x 2 y 6 Example: Solve the linear inequality by graphing. y 3 We will now solve systems of linear inequalities. Solving Systems Linear Inequalities Graphically 1. For each inequality: graph the boundary line. • Solve the inequalities for y *** Remember to flip the sign if you multiply or divide both sides by a negative number *** • Graph each using the slope and y-intercept • Solid line if or • Dashed line if < or > 2. For each inequality: determine which side of the boundary line to shade. • For each: pick a test point that does not fall on the boundary line • True statement – shade that side • False statement – shade the other side 3. Clearly indicate the solution for the system (where the solution sets overlap) Example: Solve the system of linear equations by graphing. 2 x y 3 x 2 y 1 Example: Solve the system of linear equations by graphing. 3x y 2 y 3(1 x) Example: Match each equation, inequality or system with its graph. x y 2 x y 2 x y 2 x y 2 x y 2 x 2 2