Systems of Linear Systems of Linear Inequalities (4.10)Inequalities (4.10)

Layering inequalities Layering inequalities

PODPOD

Graph the following inequality neatly on Graph the following inequality neatly on graph paper.graph paper.

y < 2x – 5y < 2x – 5

What steps do you take to graph it?What steps do you take to graph it?

How could you graph it on your How could you graph it on your calculator?calculator?

Add another inequalityAdd another inequality

On top of the On top of the inequality you just inequality you just graphed, add this graphed, add this one.one.

y y ≤ -(1/3)x + 3≤ -(1/3)x + 3

Add another inequalityAdd another inequality

On top of the On top of the inequality you inequality you just graphed, just graphed, add this one.add this one.

y y ≤ -(1/3)x + 3≤ -(1/3)x + 3

Solution setSolution set

y < 2x – 5y < 2x – 5y y ≤ -(1/3)x + 3≤ -(1/3)x + 3

Looking at this graph, Looking at this graph, what do you think the what do you think the solution set is?solution set is?

What is the “max” point?What is the “max” point?

How could you find the How could you find the point algebraically?point algebraically?

How could you use your How could you use your calculator to find that calculator to find that point?point?

Solution setSolution set

y < 2x – 5y < 2x – 5

y y ≤ -(1/3)x + 3≤ -(1/3)x + 3

To find the “max” To find the “max” point algebraically,point algebraically,

Set the equations Set the equations equal to each equal to each other– find x, then other– find x, then plug it in to find y plug it in to find y for the point of for the point of intersection.intersection.

Solution setSolution set

y < 2x – 5y < 2x – 5y y ≤ -(1/3)x + 3≤ -(1/3)x + 3

You can also use the You can also use the calc-intersect calc-intersect function, you can function, you can find the point in the find the point in the solution set that solution set that “maximizes” both “maximizes” both equations.equations.

How do these values How do these values compare to what compare to what you got you got algebraically?algebraically?

Try itTry it

Use the same process of graphing Use the same process of graphing and finding the intersection to and finding the intersection to find the max point of the find the max point of the following system. Find the point following system. Find the point with algebra, then check with with algebra, then check with your calculator.your calculator.

5x – 2y < 105x – 2y < 10x + y < 4x + y < 4

Try itTry it

5x – 2y < 105x – 2y < 10x + y < 4x + y < 4

Rewrite for Rewrite for calculator:calculator:

y > (5/2)x – 5y > (5/2)x – 5y < -x + 4y < -x + 4

Try itTry it

5x – 2y < 105x – 2y < 10x + y < 4x + y < 4

For calculator:For calculator:y > (5/2)x – 5y > (5/2)x – 5y < -x + 4y < -x + 4

What is the max point What is the max point for this graph?for this graph?