Graphs Of Linear Inequalities Worksheet With Answers Page 10
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Example 8:
Graph the following system of linear inequalities.
3
3
y
> −
x
+
2
x y
− >
4
Solution:
We first write the inequality
3
+ as an equation,
3
3
+ . The line will be
3
y
> −
x
y
= −
x
graphed as a dashed line because the inequality is > , which does not include the line. We will
graph the line using x- and y-intercepts.
y
= −
3
x
+
3
y
= −
3
x
+
3
( )
0
= −
3
x
+
3
y
= −
3 0
+
3
3
x
3
y
3
=
=
x
=
1
(
)
(
)
A dashed line is drawn through the intercepts, which are located at
1, 0 and
0, 3 . Since the
inequality is of the form
y
> −
3
x
+ , we shade above the line.
3
Math 1313
Page 10 of 21
Section 1.4
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