Graphs Of Linear Inequalities Worksheet With Answers Page 12
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Example 9:
Graph the following system of linear inequalities.
−
12
x
+
3
y
> −
6
−
3
x y
− ≥
3
Solution:
We first write the inequality 12
−
x
+
3
y
> − as an equation, 12
6
−
x
+
3
y
= − . The line
6
will be graphed as a dashed line because the inequality in this problem is > , which does not
include the line. We will graph the line using x- and y-intercepts.
12
3
6
12
3
6
−
x
+
y
= −
−
x
+
y
= −
( )
( )
−
12
x
+
3 0
= −
6
−
12 0
+
3
y
= −
6
−
12
x
= −
6
3
y
= −
6
1
x
=
y
= −
2
2
1
(
)
A dashed line is drawn through the intercepts, which are located at
, 0
and
0, 2 . We then
2
need to decide whether to shade above or below the line. Instead of choosing a test point, we can
isolate the variable y on the left-hand side of 12
3
> − and determine which half-plane to
6
−
x
+
y
shade.
−
12
x
+
3
y
> −
6
3
y
>
12
x
−
6
y
>
4
x
−
2
Since the inequality is of the form
y
>
4
x
− , we shade above the line.
2
Math 1313
Page 12 of 21
Section 1.4
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