Transcript Linear Equations Lesson 2.3 Equations  Definition:    A statement that two mathematical expressions are equal An equation always contains an equals sign = Examples x -7  3

Linear Equations
Lesson 2.3
Equations

Definition:
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
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A statement that two mathematical expressions are
equal
An equation always contains an equals sign =
Examples
x -7  3 x  5
x  y  x2  y3  x
1  2  17
The statement may be
true or false.
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Solving Equations

Searching for value(s) of the variable(s) which
make the statement true
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Called the "solution set"
Some equations have no solutions
Called a
contradiction
x+1=x
Some equations have multiple solutions
2x + 16 = 2(x + 8)
x2 = 9
x + y = 21
This one is referred
to as an identity
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Linear Equation in One
Variable
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Format: the equation can be written
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a and b are real numbers
a≠0
ax b  0
Solved by manipulating both sides of the
equation
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Add same quantity
to both sides
Multiply both sides
by same quantity
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Graphical Solution

Treat the equation as
two separate functions
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1
2 x  3.5   x  4
2
Each side of the equals sign
Specify each side as a function in the Y = screen
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Graphical Solution
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Note the intersection(s)
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Sometimes can be determined by observation
Otherwise ask calculator to determine
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Graphical Solution
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Calculator will ask you to specify
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Which lines to use
Lower and upper bounds
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Graphical Solution
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The x-value is the solution to our original
equation
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Numeric Solution
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Given
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3 x
 2 x  96
2
Let each side be a function
Place in Y= screen of calculator
View table ♦Y,
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Adjust starting point, increment
Narrow down search, adjust again
Look for matches
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Assignment A
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
Lesson 2.3A
Page 126
Exercises 1 – 73 EOO
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Problem Solving
Strategies
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Jot down important facts
Draw a picture
Assign a variable to what you want to solve for
Write an equation that represents the
relationships described
Solve the equation
Make sure that you have answered the original
question – sometimes it is some other form of
the equation solution
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Example

A person 66 inches tall is standing 15 ft from a
streetlight. If the person casts a shadow 84
inches long, how tall is the streetlight?
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Another Example

At 2:00 a runner heads north on a highway
jogging at 10 mph. At 2:30 a driver heads north
on the same highway to pick up the runner. The
car was traveling at 55 mph. How long will it
take the driver to catch the runner?
Remember that Dist = Rate * Time
Hint: What two things are equal so we
can write an equation?
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Assignment B

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Lesson 2.3B
Page 128
Exercises 91 – 107 EOO
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