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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 ... – PowerPoint PPT presentation

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


1
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.
2
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
3
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.
4
Example 1 Checking Solutions of a Linear
System Check whether the following are solutions
to the system a) (2, 2) b) (0, -1)
5
Solution a)
Since (2, 2) is a solution of each equation, it
is a solution of the system of equation.
6
Solution b)
Since (0, -1) is not a solution of equation 2, it
is not a solution of the system.
7
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
8
Example 2 Solving a system graphically.   Solve
the system.
9
Step 1) Begin by graphing both
equations.
Equation 1
Equation 2
10
From the graph, the lines appear to intersect at
(2, 1).
11
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).
12
Systems of Equations may have infinite number of
solutions. If the two equations are equivalent
they represent the same line.
13
Example 3 Tell how many solutions the linear
system has. a)
14
Graph the equations.
These equations represent the same line.
15
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.
16
Tell how many solutions the linear system has.
17
Graph the two equations.
18
If two lines are parallel they have the same
slope but different y-intercepts.
19
Homework Page 143 12 46 even, 53 - 55 all
20
A system of equations may have no solutions in
common. If two lines never intersect, then they
are parallel.
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