Graphs Of Linear Inequalities Worksheet With Answers Page 20
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2
3
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5
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9
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18
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21
y
≥ −
18
x
+
9
The system of inequalities is:
x
<
3
− ≤ <
2
y
9
The inequalities may be written in an another equivalent form. For example, we can also state the
18
x y
+ ≥
9
system of inequalities as:
x
<
3
− ≤ <
2
y
9
***
Example 14:
Write the system of inequalities that corresponds to the following graph.
Solution:
First, we need to find the equation of each line. We will use the slope and y-intercept,
and write each line in the form y mx b
=
+ .
(
)
(
)
Line 1 passes through the point
0, 5 , so
b = . Since the line also passes through
5
1, 0 ,
y
−
y
0 5
−
2
1
m
=
=
= −
5
. The equation for Line 1 is
y
= −
5
x
+ .
5
x
−
x
1 0
−
2
1
(
)
(
)
Line 2 passes through the point
0, 2 , so
b = . Since the line also passes through
2
4, 0 ,
y
−
y
0 2
−
−
2
1
1
2
1
m
=
=
=
= −
. The equation for Line 2 is
y
= −
x
+ .
2
x
−
x
4 0
−
4
2
2
2
1
Also notice that the shaded region is bounded by the y-axis (
x = ) and the x-axis (
0
y = ).
0
We now need to determine the inequalities. The shaded region lies below Line 1 and the line is
1
solid, so
y
≤ −
5
x
+ . The shaded region lies below Line 2 and the line is solid, so
5
y
≤ −
x
+ .
2
2
Math 1313
Page 20 of 21
Section 1.4
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