# 2.6 2.6 Linear Inequalities in Two Variables Linear Inequalities in Two Variables

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```2.6 Linear Inequalities in Two Variables
A linear iinequality
nequality in two variables is an inequality that can be written in one of the
following forms:
Ax + By &lt; C
Ax + By &gt; C
Ax + By &lt; C
Ax + By &gt; C
An ordered pair (x, y) is a solut
olution
ion of a linear inequality if the inequality is true when
the values of x and y are substituted into the inequality.
Ex:
Ex: Determine if each point is a solution to 4x – 2y &gt; 8.
a) (3, 3)
b) (−2, −9)
c) (0, 0)
Graphing Linear Inequalities
1.) Graph the “boundary” line.
• Use a solid line if &lt; or &gt;
• Use a dashed line if &lt; or &gt;
2.) Pick a test point on either side of the line, not a point directly on the boundary line.
If it is a solution, shade the region that contains the point.
**NOTE:
**NOTE: All points in shaded region are solutions to inequality.
Ex:
Ex: Graph each inequality.
d) y &lt; 2
e) x &gt; −1
f) 4x + 2y &gt; 8
Your turn…
g) x &gt; 5
j) 2x – 5y ≥ 10
h) y &lt; – 4
k) 3x + y ≤ 6
i) y ≥ –x + 7
l) 3x – y &lt; 3
```