Bellwork

Write a “system” of inequalities for the shaded region in the graph at right.

(Hint: you should have 4!)

3-3 Systems of Inequalities(p. 133)

Algebra 2

Prentice Hall, 2007

Objectives

You will… Solve a system of linear inequalities by

graphing. Model a real-world example with a system

in inequalities and solve it by graphing.

Solving

To solve a system of inequalities: Graph and shade each inequality on the same

coordinate plane. The “overlapping” part is the solution of the

system.

Ex. 1 Solve the system:

€

x + y ≤ 6

−x − 4y < 8

⎧ ⎨ ⎩

Solving

€

x + y ≤ 6

−x − 4y < 8

⎧ ⎨ ⎩

10

8

6

4

2

-2

-4

-6

-8

-10

-10 -5 5 10

Solving

Ex. 2 Solve the system 10

8

6

4

2

-2

-4

-6

-8

-10

-10 -5 5 10

€

x ≥ y − 3

y ≥ x − 2 +1

⎧ ⎨ ⎩

Real-World Example

Ex. 3 You are in charge of a fall bake sale fundraiser. You want to bake at least 6 and at most 11 loaves of bread. You also want at least twice as many loaves of pumpkin bread as cranberry bread. Write a system of inequalities to model this

situation. Graph the system to find the solution set. Analyze your graph to be sure you know how

many loaves of each type of bread you should bake.

Real-World Example

Ex. 3 You are in charge of a fall bake sale fundraiser. You want to bake at least 6 and at most 11 loaves of bread. You also want at least twice as many loaves of pumpkin bread as cranberry bread. Write a system of inequalities to model this

situation.HINTS:

• Define your variables 1st!

• Write as many inequalities as necessary.

Real-World Example

Ex. 3 contin. Write a system of inequalities to model this

situation. Graph the system to find the solution set.

HINT: Declare an independent vs. dependent variable!

Real-World Example

Ex. 3 contin. 12

10

8

6

4

2

-2

-4

-5 5 10

Real-World Example

Ex. 3 contin. Write a system of inequalities to model this

situation. Graph the system to find the solution set. Analyze your graph to be sure you know how

many loaves of each type of bread you should bake.

HINT: Since you can’t bake half a loaf, the solution is a “finite” set. List ALL the possible combinations!

Assignment

3-3 p. 136: mo6 (6-24); 40, 45, 49 or 52 b