Systems of Linear Inequalities (4.10) Layering inequalities

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

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

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

Solution set y < 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?

Solution set y < 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.

Solution set y < 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?

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 < 10 x + y < 4

Try it 5x – 2y < 10 x + y < 4 Rewrite for calculator: y > (5/2)x – 5 y < -x + 4

Try it 5x – 2y < 10 x + y < 4 For calculator: y > (5/2)x – 5 y < -x + 4 What is the max point for this graph?