25 Solving Systems of Linear Inequalities
Warm Up
Solve each inequality for y.
1.
8x + y < 6
2. 3x – 2y > 10
3. Graph the solutions of 4x + 3y > 9.
Holt McDougal Algebra 1
25 Solving Systems of Linear Inequalities
Objective
I can graph and solve systems of linear
inequalities in two variables.
A system of linear inequalities
is a set of two or more linear
inequalities containing two or
more variables. The solutions of
a system of linear inequalities
are all the ordered pairs that
satisfy all the linear inequalities in
the system.
Holt McDougal Algebra 1
25 Solving Systems of Linear Inequalities
Example 1: Identifying Solutions of Systems of
Linear Inequalities
Tell whether the ordered pair is a solution of
the given system.
(–1, –3);
y ≤ –3x + 1
y < 2x + 2
Remember!
An ordered pair must be a
solution of all inequalities to be a
solution
Holt McDougal
Algebra 1of the system.
25 Solving Systems of Linear Inequalities
Remember when you used to graph two
inequalities on a number line?
x ≥ -2 and x < 3
-10-9-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Where they overlap is the solution.
-10-9-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Holt McDougal Algebra 1
25 Solving Systems of Linear Inequalities
To show all the solutions of a system of linear
inequalities, graph the solutions of each inequality.
The solutions of the system are represented by the
overlapping shaded regions. Below are graphs of
Examples 1A and 1B on p. 435.
Holt McDougal Algebra 1
25 Solving Systems of Linear Inequalities
We can do the same thing with the coordinate plane and
linear inequalities. Remember, to know where to shade you
can pick a test point like (0,0).
Example 2
Graph
y ≥ -x + 2
2x + 4y < 4
Y
X
Holt McDougal Algebra 1
25 Solving Systems of Linear Inequalities
Example 3
y>x-2
1
y
x3
3
Y
X
Holt McDougal Algebra 1
25 Solving Systems of Linear Inequalities
Example 4: Graphing Systems with Parallel Boundary
Lines
Graph the system of
y ≤ –2x – 4
linear inequalities.
y > –2x + 5
Describe the solutions.
Y
X
Holt McDougal Algebra 1
25 Solving Systems of Linear Inequalities
Example 5: Graphing Systems with Parallel Boundary
Lines
Graph the system of
linear inequalities.
Describe the
solutions.
y < 3x + 6
y > 3x – 2
Y
X
Holt McDougal Algebra 1
25 Solving Systems of Linear Inequalities
Caution
An ordered pair solution of the system need not
have whole numbers, but answers to many
application problems may be restricted to whole
numbers.
Example 6
At her party, Alice is serving pepper jack cheese
and cheddar cheese. She wants to have at least
2 pounds of each. Alice wants to spend at most
$20 on cheese. Show and describe all possible
combinations of the two cheeses Alice could
buy. List two possible combinations.
Price per Pound ($)
Pepper Jack
4
Cheddar
2
Let x =
and y =
She wants at least 2
pounds of pepper jack.
She wants at least 2
pounds of cheddar.
Holt McDougal Algebra 1
She wants to spend no
more than $20.
25 Solving Systems of Linear Inequalities
Example 6 Continued
Step 2 Graph the system.
Y
X
Holt McDougal Algebra 1
25 Solving Systems of Linear Inequalities
Step 3 Describe all possible combinations.
All possible combinations within the gray region will
meet Alice’s requirement of at most $20 for cheese
and no less than 2 pounds of either type of cheese.
Answers need not be whole numbers as she can
buy fractions of a pound of cheese.
Step 4 Two possible combinations are…….
Holt McDougal Algebra 1
25 Solving Systems of Linear Inequalities
Assignment
25 Reading Strategies
25 Review for Mastery
Holt McDougal Algebra 1