3-1: Solving Linear Systems by Graphing (Day 1)

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3-1 Solving Linear Systems by Graphing (Day 1)
Objective CA 2.6 Students solve systems of
linear equations and inequalities (in two or
three variables) by substitution, graphs, or
matrices.
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A system of two linear equations in two variables
x and y consists of two equations of the
following form Ax By C Dx Ey F
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If two lines intersect, how many points do both
lines have in common?
One
The point of intersection (x, y) must be a valid
solution to both line equations.
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Example 1 Checking Solutions of a Linear
System Check whether the following are solutions
to the system a) (2, 2) b) (0, -1)
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Solution a)
Since (2, 2) is a solution of each equation, it
is a solution of the system of equation.
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Solution b)
Since (0, -1) is not a solution of equation 2, it
is not a solution of the system.
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Solving a System of equations by Graphing
Step 1 Get in slope-intercept form
Step 2 Graph each equation
Step 3 Identify where graphs
intersect
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Example 2 Solving a system graphically.   Solve
the system.
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Step 1) Begin by graphing both
equations.
Equation 1
Equation 2
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From the graph, the lines appear to intersect at
(2, 1).
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From the graph, the lines appear to intersect at
(2, 1). Check this algebraically by substitution
into the original equations.
The solution is (2, 1).
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Systems of Equations may have infinite number of
solutions. If the two equations are equivalent
they represent the same line.
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Example 3 Tell how many solutions the linear
system has. a)
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Graph the equations.
These equations represent the same line.
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If the two equations are of the same line they
will have the same equation when converted to the
slope intercept form of the linear equation.
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Tell how many solutions the linear system has.
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Graph the two equations.
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If two lines are parallel they have the same
slope but different y-intercepts.
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Homework Page 143 12 46 even, 53 - 55 all
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A system of equations may have no solutions in
common. If two lines never intersect, then they
are parallel.