This document provides instructions for graphing systems of linear inequalities: - Graph each inequality individually by plotting points, drawing the line, and shading the correct region based on whether it is <, ≤, >, or ≥ - Find the overlapping region that satisfies both inequalities, which is the solution to the full system - An example graphs two inequalities and finds the overlapping purple region as the solution - Vertices can be found by setting the equations of intersecting lines equal to each other

1. Graphing Systems of Inequalities

3. Inequalities with Greater Than Pick a point from the shaded region and test that point in the equation y = x + 3 . Point: (-4, 5) This is incorrect. Five is greater than or equal to negative 1. If a solid line is used, then the equation would be 5  -1 . If a dashed line is used, then the equation would be 5 > -1 . The area above the line is shaded .

4. Inequalities with Less Than Pick a point from the shaded region and test that point in the equation y = -x + 4 . Point: (1, -3) This is incorrect. Negative three is less than or equal to 3. If a solid line is used, then the equation would be -3  3 . If a dashed line is used, then the equation would be -3 < 3 . The area below the line is shaded .

6. Example Graph the following linear system of inequalities. Use the slope and y-intercept to plot two points for the first inequality. Draw in the line. For  use a solid line. Pick a point and test it in the inequality. Shade the appropriate region. x y

7. Example Graph the following linear system of inequalities. The region above the line should be shaded. Now do the same for the second inequality. x y

8. Example Graph the following linear system of inequalities. Use the slope and y-intercept to plot two points for the second inequality. Draw in the line. For < use a dashed line. Pick a point and test it in the inequality. Shade the appropriate region. x y

9. Example Graph the following linear system of inequalities. The region below the line should be shaded. x y

10. Example Graph the following linear system of inequalities. The solution to this system of inequalities is the region where the solutions to each inequality overlap. This is the region above or to the left of the green line and below or to the left of the blue line. Shade in that region. x y

11. You Try It Graph the following linear systems of inequalities.

12. Problem 1 Use the slope and y-intercept to plot two points for the first inequality. Draw in the line. Shade in the appropriate region. x y

13. Problem 1 Use the slope and y-intercept to plot two points for the second inequality. Draw in the line. Shade in the appropriate region. x y

14. Problem 1 The final solution is the region where the two shaded areas overlap (purple region). x y