Solving Equations Numerically

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Technology 2.1
Solving Equations Numerically
Figure 2.1a
Rename the independent variable x if necessary.
For Figure 2.1a, Set up the table. Set up the
column for the independent variable, x, by
setting a minimum integer value 0 and increments
of 1 for integers.
2nd
TBLSET
(Minimum number in the table is 0.) (Values of
independent variable are increasing by 1.)
0
ENTER
1
ENTER
Set the calculator to perform the operations
automatically.
ENTER
ENTER
?
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Technology 2.1
Solving Equations Numerically
Figure 2.1b
For Figure 2.1b, Set up the second column to be
the expression on the left side by entering the
left expression of the equation, 2x 3, in Y1.
ENTER
3

2
Y
X,T,?,n
Set up the third column to be the expression on
the right side by entering the right expression
of the equation, x 5, in Y2.
5

X,T,?,n
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3
Technology 2.1
Solving Equations Numerically
Figure 2.1c
For Figure 2.1c, View the table. Move beyond
the screen to view additional rows by using the
up and down arrows. The solution is the x-value
that results in equal Y1 and Y2 values. The
solution of 2x 3 x 5 is 2 because 7 7.
2nd
TABLE
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Technology 2.4
Solving Equations Graphically
Solve 2x 3 x 5 graphically.
Figure 2.4a
Rename the independent variable x if necessary.
Enter the expression on the left side of the
equation, 2x 3, as Y1.
For Figure 2.4a,

3
2
Y
ENTER
X,T,?,n
Enter the expression on the right side of the
equation, x 5, as Y2.
5

X,T,?,n
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5
Technology 2.4
Solving Equations Graphically
Y2 x 5
Y1 2x 3
Solve 2x 3 x 5 graphically.
(-10, 10, -10, 10)
For Figure 2.4b,
Figure 2.4b
Graph the equations. (In this case, we will use
the standard window.)
ZOOM
6
Find the intersection of the graphs. First trace
the graph.
TRACE
Use the arrow keys to find the intersection. If
the intersection cannot be found by tracing, use
INTERSECT, option 5, under the CALC menu.
ENTER
ENTER
ENTER
CALC
2nd
5
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Technology 2.4
Solving Equations Graphically
Solve 2x 3 x 5 graphically.
Figure 2.4c
For Figure 2.4c,
The solution is the x-value of the intersection
point and is stored in x. The y-coordinate of
the point of intersection is the value obtained
for both the left side (Y1) and the right side
(Y2) and is also stored. We can use this feature
to check whether Y1 equals Y2. Quit the graph
screen and enter x.
ENTER
QUIT
2nd
X,T,?,n
Enter Y1 and Y2.
VARS
ENTER
ENTER
VARS
2
1
1
1
?
?
Since x 2 when 7 7 (or Y1 Y2), the solution
of 2x 3 x 5 is 2.
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Technology 2.6
Graphing Number Lines
Figure 2.6a
(-10, 10, -10, 10)
Figure 2.6b
For Figure 2.6a, Enter the inequality x lt 5 in
Y1. The inequality symbols are found under the
TEST menu. The less than symbol is option 5.
Y
5
2nd
5
TEST
X,T,?,n
For Figure 2.6b, Graph the number line. The
calculator will test the inequality for x-values
and graph an ordered pair (x, 1) for a true
inequality and (x, 0) for a false inequality.
ZOOM
6
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Technology 2.6
Graphing Number Lines
(-10, 10, -10, 10)
Figure 2.6c
For Figure 2.6c, Trace and use the arrow keys to
display the coordinates graphed. To check
the lower bound of a number line, 5, enter the
value while tracing.
TRACE
ENTER
5
If the lower bound is a solution of the
inequality, it will have a y-coordinate of 1. If
the lower bound is not a solution of the
inequality, it will have a y-coordinate of 0.
For x lt 5, the lower bound is not a solution and
is graphed as (5, 0).
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