3­1 Graphing Systems of Equations web.notebook
3.1 Graphing Systems of
Equations
October 13, 2008
Check Skills You'll Need:
Graph each equation. Use one coordinate plane for all three graphs.
1. 2x - y = 1
OBJECTIVES
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2. 2x - y = -1
3. x + 2y = 2
Jul 31­1:28 PM
System of Equations:
Two or more equations that use the same variables.
1
y = x + 1
2
What values of x and y will
satisfy BOTH of these
equations?
3
y = x ­ 1
How do we figure it out?
2
Jul 31­1:29 PM
Graph these two equations to find their intersection.
1
y = x + 1
2
3
y = x ­ 1
2
Intersection:
(2, 2)
Answer is hiding!
Graph both equations!
Jul 31­1:41 PM
Jul 31­1:44 PM
What is the solution to this system of equations?
So what does the point ﴾2, 2﴿ mean?
1
y = x + 1
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
y = x + 3
1
y = ­ x
2
Solution:
(­2, 1)
Jul 31­1:47 PM
1
3­1 Graphing Systems of Equations web.notebook
Types of linear systems
Two intersecting lines:
one solution
Parallel lines:
no solutions
October 13, 2008
Use this system of equations:
Same line:
Many solutions
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.
DEPENDENT
INDEPENDENT
INCONSISTENT
Jul 31­1:50 PM
Jul 31­1:54 PM
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
HOMEWORK
p. 120 #1-9, 13-24, 46-48,
73, 74
Jul 31­1:56 PM
2