Graphing Method. Graph of x + y < > y 10. x

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2 Graphing Method Eample: Graph the inequalities on the same plane: + < 6 and 2 - > 4. Before we graph them simultaneousl, let s look at them separatel Graph of + < > -10

3 Graphing Method This is: 2 - > So what happens when we graph both inequalities simultaneousl? -10

4 Coolness Discovered! Wow! The solution to the sstem is the brown region - where the two shaded areas coincide. The green region and red regions are outside the solution set

5 So what were the steps? Graph first inequalit Shade lightl (or use colored pencils) Graph second inequalit Shade lightl (or use colored pencils) Shade darkl over the common region of intersection. That is our solution!

6 1. Write the inequalities in slope-intercept form. 2. Use the slope and -intercept to plot the lines. 3. Draw in the line. Use a solid line for less than or equal to () or greater than or equal to ( ). Use a dashed line for less than (<) or greater than (>). 4. Pick a point above the line or below the line. Test that point in the inequalit. If it makes the inequalit true, then shade the region that contains that point. If the point makes the inequalit false, shade the region on the other side of the line. (Don t forget to flip the sign if ou divide b a negative #) -Hint: > or shade above < or shade below 1. Sstems of inequalities Follow steps 1-4 for each inequalit. Find the region where the solutions to the two inequalities would overlap and this is the region that should be shaded.

7 Graph the following linear sstem of inequalities Use the slope and - intercept to plot two points for the first inequalit. Draw in the line. For use a solid line. Pick a point and test it in the inequalit. Shade the appropriate region.

8 Graph the following linear sstem of inequalities Point (0,0) 0 2(0) The region above the line should be shaded. Now do the same for the second inequalit.

9 Graph the following linear sstem of inequalities Use the slope and - intercept to plot two points for the second inequalit. Draw in the line. For < use a dashed line. Pick a point and test it in the inequalit. Shade the appropriate region.

10 Graph the following linear sstem of inequalities (-2) < 8 Point (-2,-2) The region below the line should be shaded.

11 Graph the following linear sstem of inequalities The solution to this sstem of inequalities is the region where the solutions to each inequalit 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.

12 Graph the following linear sstems of inequalities

13 2 4 Use the slope and - intercept to plot two points for the first inequalit. Draw in the line. Shade in the appropriate region.

14 2 4 Use the slope and - intercept to plot two points for the second inequalit. Draw in the line. Shade in the appropriate region.

15 2 4 The final solution is the region where the two shaded areas overlap (purple region).

16 Graphing a Sstem of Two Inequalities Graph the sstem of linear inequalities Dotted line 6 Dotted line 0 6 2

17 Graphing a Sstem of Two Inequalities Graph the sstem of linear inequalities Solid line 3 Dotted line

18 Graphing a Sstem of Two Inequalities Graph the sstem of linear inequalities Solid line 1 Dotted line

19 Graphing a Sstems of Inequalities Graph the sstem of inequalities > /3 + 1 Identif three solution points

20 Finding Solution Points Graph the sstem of inequalities < 5 Identif two solution points > - 2

21 Graphing a Sstem of Three Inequalities Graph the sstem of linear inequalities Solid lines

22 Graphing a Sstem of Three Inequalities Graph the sstem of linear inequalities Solid lines

23 Graphing a Sstem of Three Inequalities Graph the sstem of linear inequalities Dotted lines 2 Solid lines