Name: ________________________________________
Date: _____________
8.5 Systems of Inequalities
Objectives: I will be able to:
Linear inequality
in 2 variables:
Solution:
A linear inequality in x and y is an inequality that can be written in one of the following
forms. Ax + By  C where  can be replace with <, ≤ , >,or ≥.
Solution of a linear inequality in 2 variables is an ordered pair
(x, y) that when plugged in, makes the statement TRUE.
Example 1:
Graphing a Linear Inequality in Two
Variables
1. Replace the inequality symbol
with an equal sign and graph the
corresponding linear equation.
Draw a solid line if the original
inequality contains a < or >
symbol. Draw a dashed line if
the original inequality contains a
< or > symbol.
2. Choose a test point in one of
the half-planes that is not on the
line. Substitute the coordinates
of the test point into the
inequality
3. If a true statement results,
shade the half-plane containing
this test point. If a false
statement results, shade the halfplane not containing this test
point.
a) Graph
3x -5 y <15
Now You Try:
b) Graph
y <5
d) Graph
4x - 2 y ³ 8
e) Graph
x +2y ³0
c) Graph
x ³ -4
Example 2:
a) Graph
x 2 + y 2 £16
b) Graph
x 2 + y 2 > 25
c) Graph
y ³ log3( x -1)
System of
Inequalities:
Example 3:
Now You Try:
Show that point B is a solution of the system.
Example 4:
ì2 x + y < 8
í
a) Graph
îx + y ³ 4
b) Graph
Example 5:
ìx - y < 2
ï
í2 £ x < 4
ïy <3
î
Graph the solution set of the system:
ì y ³ x2 -9
í
îx - y > 3
Now You Try:
ìï x 2 + y 2 < 4
í
ïî y - x 2 ³ 0
Example 6:
Write a system of inequalities for each graph.
a)
b)
Now You Try:
c)
Practice Plus:
68. Write the given sentences as a system
of inequalities in two variables. Then
graph the system.
The sum of the squares of the x-variable
and the y-variable is no more than 25.
The sum of twice the y-variable and the
x-variable is no less than 5.
70. Rewrite each inequality in the system
without absolute value bars. Then graph
the rewritten system in rectangular
coordinates.
ìx £3
ï
í
ïî y £ 5
72. Graph the union of
x - y ³ -1 and
5x - 2 y £10
Without graphing, in Exercises 73–76, determine if each system has no solution or
infinitely many solutions.
SUMMARY:
Assignment:
Pg. 847 – 850: # 3, 11, 15 -= 19, 23, 25, 29, 39, 47, 51, 55, 61, 67, 69, 75 – 79 Odd