Download 3.1 Solve Linear Systems by Graphing

3.1
Solve Linear Systems by
Graphing
Goal
Your Notes
p Solve systems of linear equations.
VOCABULARY
System of two linear equations
Solution of a system
Consistent
Inconsistent
Independent
Dependent
Example 1
Solve a system graphically
Graph the system and estimate
the solution. Then check the
solution algebraically.
y
1
4x 1 2y 5 4
2x 2 3y 5 10
Equation 1
Equation 2
1
x
Solution
Graph both equations. The lines appear to intersect at
(
,
). Check this algebraically as follows:
Remember to check
the visual solution
in both equations.
4(
Equation 1
Equation 2
4x 1 2y 5 4
) 1 2(
)04
54✓
2x 2 3y 5 10
) 2 3(
) 0 10
5 10 ✓
Copyright © Houghton Mifflin Harcourt Publishing Company.
All rights reserved.
2(
Lesson 3.1 • Algebra 2 Notetaking Guide
3-57
Your Notes
Checkpoint Graph the linear system and estimate the
solution. Then check the solution algebraically.
4x 1 y 5 22
1.
y
1
26x 2 3y 5 12
x
1
NUMBER OF SOLUTIONS OF A LINEAR SYSTEM
Exactly one solution
y
Infinitely many
solutions
No solutions
y
x
Lines intersect at
y
x
Lines
;
consistent and
x
Lines are
;
consistent and
Example 2
Solve a system with many solutions
Solve the system. Then classify the system as
consistent and independent, consistent and dependent,
or inconsistent.
22x 1 y 5 4
4x 2 2y 5 28
Equation 1
Equation 2
The graphs of the equations are
. So, each point on
the line is a solution, and the system
has
solutions.
Therefore, the system is
.
58
Lesson 3.1 • Algebra 2 Notetaking Guide
y
1
1 x
Copyright © McDougal Littell/Houghton Mifflin Company.
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