6-8 Systems of Linear Inequalities Select 2 colored pencils that blend together to produce a third distinct color! Algebra 1 Glencoe McGraw-HillLinda Stamper

Do you remember how to graph an inequality? Two or more linear inequalities in the same variables form a system of linear inequalities. A solution of a system of linear inequalities in two variables is an ordered pair that is a solution of each inequality in the system. When graphing a system of linear inequalities, graph each inequality in the same coordinate plane. Systems of Linear Inequalities

Graphing A Linear Inequality x y The graph of a linear inequality in two variables is the graph of the solutions of the inequality. A boundary line divides the coordinate plane into two half-planes. The solution of a linear inequality in two variables is a half-plane. Shade the side of the half-plane that contains the solutions.

x y The graph of a linear inequality in two variables is the graph of the solutions of the inequality. A boundary line divides the coordinate plane into two half-planes. The solution of a linear inequality in two variables is a half-plane. Shade the side of the half-plane that contains the solutions. Graphing A Linear Inequality

x y Use a dashed boundary line for. A dashed line indicates that the points on the line are NOT solutions. Use a solid boundary line for. A solid line indicates that the points on the line are solutions. Graphing A Linear Inequality

1.Graph the corresponding equation, using a dashed ( ) line or a solid ( ) line. You may need to write the equation in slope-intercept form to graph the boundary line. 2. Test the coordinates of a point in one of the half-planes. You can use any point that is not on the line as a test point. 3. Shade the half-plane containing the test point if it is a solution of the inequality. If it is not a solution, shade the other half-plane. Graphing A Linear Inequality

Graph the inequality. x y boundary line false Test (0,0)

Graph the system x 2. x y Write one inequality. x < 1 Write the related equation. Graph the equation; solid boundary line. Test a point. Use (0,0) if possible. Test is true, so shade half-plane that does contain the test point. Repeat above steps to graph the other inequality on the same coordinate plane. dashed boundary line Test (0,0) Test false – shade half- plane that does not contain the test point. Would the ordered pair (1,2) be a solution of the system? It is not a solution because it must be true for both inequalities! The overlap represents the solution of the system. That is the intersection of the two inequalities! Use the inequality to test the point!

Graph each system. Example 2 – x + y > – 5 and Example 3 –x +2y > –2 and –x + 2y < 4. Example 4 y 1 and y > 2. Example 1 x > 2 and y > –3. Please copy all of the above problems in your spiral notebook!

Example 1 Graph the system x > 2 and y > –3. x y x > 2 dashed boundary line The solution is the intersection of the two inequalities! Use the inequality to test the point!

Example 2 Graph the system – x + y > – 5 and x y Test (0,0) in original inequality. Test true – shade half-plane that contains test point. Test (0,0) in original inequality. Test true – shade half-plane that contains test point. The solution is the intersection of the two inequalities!

x y Test (0,0) in original inequality. Test true – shade half-plane that contains test point. Test (0,0) in original inequality. Test true – shade half-plane that contains test point. The solution is the intersection of the two inequalities! Example 3 Graph the system –x +2y > –2 and –x + 2y < 4.

Example 4 Graph the system y 1 and y > 2. x y

Example 4 Graph the system y 1 and y > 2. x y Note the region that is the intersection of these two inequalities! The intersection of all 3 inequalities represents the solution of the system.

6-A14 Pages # 7–18, 37,