3.1 Graphing Systems of Equations 2010 October 11, 2010
3.1 Graphing Systems of
Equations
OBJECTIVES
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Jul 31­1:28 PM
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3.1 Graphing Systems of Equations 2010 October 11, 2010
Check Skills You'll Need:
Graph each equation. Use one coordinate plane for all three graphs.
1. 2x - y = 1
2. 2x - y = -1
3. x + 2y = 2
Jul 31­1:29 PM
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3.1 Graphing Systems of Equations 2010 October 11, 2010
System of Equations:
Two or more equations that use the same variables.
1 x + 1
y = 2
What values of x and y will
satisfy BOTH of these
equations?
3 x ­ 1
y = How do we figure it out?
2
Graph both equations!
Jul 31­1:41 PM
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3.1 Graphing Systems of Equations 2010 October 11, 2010
Graph these two equations to find their intersection.
1 x + 1
y = 2
3
y = x ­ 1
2
Intersection:
(2, 2)
Answer is hiding!
Jul 31­1:44 PM
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3.1 Graphing Systems of Equations 2010 October 11, 2010
So what does the point ﴾2, 2﴿ mean?
1 x + 1
y = 2
3
y = x ­ 1
2
(2, 2) is the ONLY point that satisfies BOTH equations at the same time. It is the SOLUTION for this system of equations.
Jul 31­1:46 PM
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3.1 Graphing Systems of Equations 2010 October 11, 2010
What is the solution to this system of equations?
y = x + 3
1 x
y = ­ 2
Solution:
(­2, 1)
Jul 31­1:47 PM
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3.1 Graphing Systems of Equations 2010 October 11, 2010
Types of linear systems
Two intersecting
lines:
one solution
Same line:
Many solutions
Parallel lines:
no solutions
DEPENDENT
INDEPENDENT
INCONSISTENT
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3.1 Graphing Systems of Equations 2010 October 11, 2010
Use this system of equations:
b. Tell whether the system of
a. Without graphing, describe the
relationship between the graphs of the equations has no solution,
one solutions, or many
equations.
solutions.
c. Identify the system as
dependent, independent, or
inconsistent.
Jul 31­1:54 PM
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3.1 Graphing Systems of Equations 2010 October 11, 2010
Use this system of equations:
a. Without graphing, describe the
relationship between the graphs of the
equations.
b. Tell whether the system of
equations has no solution,
one solutions, or many
solutions.
c. Identify the system as
dependent, independent, or
inconsistent.
Jul 31­1:54 PM
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3.1 Graphing Systems of Equations 2010 October 11, 2010
HOMEWORK
p. 120 #2 - 8 even,
14 - 24 even, 46-48, 73, 74
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