Systems of Linear Inequalities (4.10)

1
Systems of Linear Inequalities (4.10)

• Layering inequalities

2
POD

• Graph the following inequality neatly on graph
  paper.
• y lt 2x 5
• What steps do you take to graph it?
• How could you graph it on your calculator?

3
Add another inequality

• On top of the inequality you just graphed, add
  this one.
• y -(1/3)x 3

4
Add another inequality

• On top of the inequality you just graphed, add
  this one.
• y -(1/3)x 3

5
Solution set

• y lt 2x 5
• y -(1/3)x 3
• Looking at this graph, what do you think the
  solution set is?
• What is the max point?
• How could you find the point algebraically?
• How could you use your calculator to find that
  point?

6
Solution set

• y lt 2x 5
• y -(1/3)x 3
• To find the max point algebraically,
• Set the equations equal to each other find x,
  then plug it in to find y for the point of
  intersection.

7
Solution set

• y lt 2x 5
• y -(1/3)x 3
• You can also use the calc-intersect function, you
  can find the point in the solution set that
  maximizes both equations.
• How do these values compare to what you got
  algebraically?

8
Try it

• Use the same process of graphing and finding the
  intersection to find the max point of the
  following system. Find the point with algebra,
  then check with your calculator.
• 5x 2y lt 10
• x y lt 4

9
Try it

• 5x 2y lt 10
• x y lt 4
• Rewrite for calculator
• y gt (5/2)x 5
• y lt -x 4

10
Try it

• 5x 2y lt 10
• x y lt 4
• For calculator
• y gt (5/2)x 5
• y lt -x 4
• What is the max point for this graph?