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Systems of EquationsMiss Connell
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Now onto
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Slope of a LineO The slope a of a line through points (x1, y1)
and (x2, y2) is determined by:
O The slope of a horizontal line .
O The slope of a vertical line
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Parallel Lines
Two Parallel lines
have the same
slope
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Perpendicular Lines
Two Perpendicular
lines have slopes
that are negative
reciprocals to oneanother.
The product of
these slopes is -1.
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Equation of a LineO There are various ways ofwriting the equation of a line.Form Equation Role of Parameters Characteristic
Function
or
Standard
Can be used to
describe any
non-vertical line
General Can be used to
describe any line.
Symmetric Can be used to
describe any
oblique line that
does not pass
through the origin.
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Proof Using Analytic GeometryO When proving a geometric statement using
algebra, do the following:
O Represent the figure in a Cartesian plane
O Express the coordinates of the significant points of the
figure using variables taking into account thehypotheses of the statement.
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Graphing
You can graph a linear function using
Table of Values
Function Form
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Let`s Practice
OPage: 94
O 1, 2df, 3ac, 4be, 5, 6, 8, 10, 12
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Systems of EquationsFirst Degree
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Systems of First DegreeEquations
O The solution of systems of equation of the first degree
is the point of intersection for these two lines.
O The Point of Intersection is also described as the
solution set which is an ordered pair: (x, y)
O Systems ofEquations are equivalent if they have thesame solution set.
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Solving a Solution ofEquations
O O
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Table of ValuesO Choose Values forx and calculate values fory.
O The solution exists when both values ofyare
the same
O We can check solution by replacing back into
original equations
O This method can be time consuming and
difficult if the solution is not an integer.
O Other option: graphing on same grid to see
intersection point.
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Table ExampleO
-3
-2
-1
0
-3 1
-2 2
-1 3
0 4
-3 5 1
-2 2 2
-1 -1 3
0 -4 4
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Comparison MethodO
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Comparison ExampleO
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Substitute ExampleO
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Elimination Method1. Create, if necessary, an equivalent system of
equations in which the coefficients of one of the
variables a
re equal o
ropposite
2. Create an equation in one variable by adding orsubtracting the corresponding sides of the equationsof the system. Solve the resulting equation.
3. Substitute the value found in one of the originalequations to determine the value of the othervariable.
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Elimination ExampleO
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Solution to Linear Systems
One Solution
No Solutions
Infinite Solutions
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One SolutionO
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One Solution
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No SolutionsO
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Non-Coinciding
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Infinite SolutionsO
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Coinciding
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PracticeO
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