Chapter 7 Notetaking Guide.pdf

Example 1
Graph a System of Two Linear Inequalities
\
To check your
graph, choose a
point in the overlap
of the half-planes.
Then substitute the
coordinates into
each inequality. If
each inequality is
true, then the point
is a solution.
Graph the system of linear inequalities.
y - x ::::: -1 Inequality 1
x + 2y < 1 Inequality 2
Solution
Graph both inequalities in the same
coordinate plane. The graph of the
system is the overlap, or
------
of the two half-planes.
Example 2
J
I I 3
i
y r~;--l
1
1
+1 ~
1
i
-3 -1 1 I 3 xl
T 1
Graph a System of Three Linear Inequalities
Graph the system of linear inequalities.
y::::: - 3 Inequality 1
x < 2 Inequality 2
y < x + 1 Inequality 3
I 3
I
J
I
I­
I
I I I
Solution
The graph of y ::::: -3 is the half-plane
and the line
,.
y
3
I
i
I
The graph of x < 2 is the half-plane to
the of the line
The graph of y < x + 1 is the half-plane
the
line
--- -----
I
-3
I
1
-1
i 1
1_- t3
1
-i
3 ,
i
I
X
Finally, the graph of the system is the
, or , of the
:-:----:---:-:
three half-planes.
Lesson 7.6 . Algebra 1 Concepts and Skills Notetaking Guide 157