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
-10
-5
5
-2
-4
-6
-8
-10
10

Solving
10
Ex. 2 Solve the system
8
x  y  3

y  x  2 1
6
4
2
-10
-5
5
-2
-4
-6
-8
-10
10
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
-5
5
-2
-4
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