1. LINEAR SYSTEMS of INEQUALITIES – Graphing Method When graphing a set of linear inequalities, the solution set will be a “shared” space where the two solutions intersect. You can see where the tan and gray have a common area where they are “on top” of each other. Coordinates in that shared space will satisfy BOTH inequalities. SHARED AREA

2. LINEAR SYSTEMS of INEQUALITIES – Graphing Method When graphing a set of linear inequalities, the solution set will be a “shared” space where the two solutions intersect. You can see where the tan and gray have a common area where they are “on top” of each other. Coordinates in that shared space will satisfy BOTH inequalities. Once again you can use either slope – intercept or an ( x, y ) table to graph. SHARED AREA

3. LINEAR SYSTEMS of INEQUALITIES – Graphing Method When graphing a set of linear inequalities, the solution set will be a “shared” space where the two solutions intersect. You can see where the tan and gray have a common area where they are “on top” of each other. Coordinates in that shared space will satisfy BOTH inequalities. Once again you can use either slope – intercept or an ( x, y ) table to graph. When graphing your lines, use Dashed line for : Solid line for : ≤ or ≥ SHARED AREA

4. LINEAR SYSTEMS of INEQUALITIES – Graphing Method EXAMPLE # 1 :

5. LINEAR SYSTEMS of INEQUALITIES – Graphing Method EXAMPLE # 1 : xY

6. LINEAR SYSTEMS of INEQUALITIES – Graphing Method EXAMPLE # 1 : xY 0- 2 I replace the inequality with an equal sign when getting my ( x, y ) points. That way I don’t get confused when solving…

7. LINEAR SYSTEMS of INEQUALITIES – Graphing Method EXAMPLE # 1 : xY 0- 2 3-4 I replace the inequality with an equal sign when getting my ( x, y ) points. That way I don’t get confused when solving…

8. LINEAR SYSTEMS of INEQUALITIES – Graphing Method EXAMPLE # 1 : xY 0- 2 3-4 Since the equation has a ( < ) symbol, use a dashed line to graph…

9. LINEAR SYSTEMS of INEQUALITIES – Graphing Method EXAMPLE # 1 : xY 0- 2 3-4 To find the side to shade, use a test point to find TRUE or FALSE… ALWAYS shade the TRUE side… I like to use ( 0, 0 ) TEST POINT

10. LINEAR SYSTEMS of INEQUALITIES – Graphing Method EXAMPLE # 1 : xY 0- 2 3-4 Since the test point is FALSE, we will shade the other side that does not contain the test point… FALSE

11. LINEAR SYSTEMS of INEQUALITIES – Graphing Method EXAMPLE # 1 : xY 0- 2 3-4 Since the test point is FALSE, we will shade the other side that does not contain the test point… FALSE

12. LINEAR SYSTEMS of INEQUALITIES – Graphing Method EXAMPLE # 1 : xY 05 Let’s get our other set of points to graph…

13. LINEAR SYSTEMS of INEQUALITIES – Graphing Method EXAMPLE # 1 : xY 05 18 Let’s get our other set of points to graph…

14. LINEAR SYSTEMS of INEQUALITIES – Graphing Method EXAMPLE # 1 : xY 05 18 Let’s get our other set of points to graph… Since the equation has a ( ≥ ) symbol, use a solid line to graph…

15. LINEAR SYSTEMS of INEQUALITIES – Graphing Method EXAMPLE # 1 : xY 05 18 Again, use ( 0, 0 ) as a test point…

16. LINEAR SYSTEMS of INEQUALITIES – Graphing Method EXAMPLE # 1 : xY 05 18 Again, use ( 0, 0 ) as a test point… FALSE !!! So shade the side that does not contain the test point… FALSE

17. LINEAR SYSTEMS of INEQUALITIES – Graphing Method EXAMPLE # 1 : xY 05 18 Again, use ( 0, 0 ) as a test point… FALSE !!! So shade the side that does not contain the test point… FALSE

18. LINEAR SYSTEMS of INEQUALITIES – Graphing Method EXAMPLE # 1 : You can see where the two colors overlap… That is the solution area. ANY coordinate point in that “shared area” will satisfy both inequalities… SHARED AREA

19. LINEAR SYSTEMS of INEQUALITIES – Graphing Method EXAMPLE # 1 : Let’s check the point ( - 6, - 2 ) … ( - 6, - 2 ) The check coordinate satisfy’s BOTH …

20. LINEAR SYSTEMS of INEQUALITIES – Graphing Method EXAMPLE # 2 :

21. LINEAR SYSTEMS of INEQUALITIES – Graphing Method EXAMPLE # 2 : Let’s use slope – intercept this time…I still replace the inequality with an equal sign when solving for “y”…

22. LINEAR SYSTEMS of INEQUALITIES – Graphing Method EXAMPLE # 2 : Let’s use slope – intercept this time…I still replace the inequality with an equal sign when solving for “y”…

23. LINEAR SYSTEMS of INEQUALITIES – Graphing Method EXAMPLE # 2 : Let’s use slope – intercept this time…I still replace the inequality with an equal sign when solving for “y”… Equation has a ≥ sign so use a solid line…

24. LINEAR SYSTEMS of INEQUALITIES – Graphing Method EXAMPLE # 2 : Let’s use slope – intercept this time…I still replace the inequality with an equal sign when solving for “y”… Test point ( 0, 0 ) is FALSE… FALSE

25. LINEAR SYSTEMS of INEQUALITIES – Graphing Method EXAMPLE # 2 : Let’s use slope – intercept this time…I still replace the inequality with an equal sign when solving for “y”… Shade the opposite side… FALSE

26. LINEAR SYSTEMS of INEQUALITIES – Graphing Method EXAMPLE # 2 : This is already in y = mx + b form…

27. LINEAR SYSTEMS of INEQUALITIES – Graphing Method EXAMPLE # 2 : Equation has a ≥ sign so use a solid line… This is already in y = mx + b form…

28. LINEAR SYSTEMS of INEQUALITIES – Graphing Method EXAMPLE # 2 : Test point ( 0, 0 ) is TRUE…so shade the side with the test point… TRUE

29. LINEAR SYSTEMS of INEQUALITIES – Graphing Method EXAMPLE # 2 : SHARED AREA You can see where the two colors overlap… That is the solution area. Again, ANY coordinate point in that “shared area” will satisfy both inequalities…

30. LINEAR SYSTEMS of INEQUALITIES – Graphing Method EXAMPLE # 2 : Let’s check the point ( 6, - 4 ) ( 6, - 4 ) The check coordinate satisfy’s BOTH …