Chp. 6.1 ­ Graphing Systems of Equations
March 19, 2013
Date:
Chapter: Chapter 6:1 ­­> Graphing Systems of Equations
Objectives: Determine the number of solutions a system of
linear equations has
Solve systems of linear equations by graphing
Algebra I
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Chp. 6.1 ­ Graphing Systems of Equations
March 19, 2013
Notes:
The cost to begin production on a band's CD is $1500. Each CD costs $4 to produce and will sell for $10. The band wants to know how many CDs they will have to sell to earn a profit.
Graphing a system can show when a company makes a profit. Create two equations: one to represent the cost of producing the CD and one to represent the income from the CD. Graph the two equations then interpret.
*System of Equations = Two equations with two variables like the above example.
*Solution to System of Equations = Point at which the two lines meet.
Types of Solutions
1) Consistent ­­> At least one solution
2) Independent ­­> Exactly one solution
3) Dependent ­­> Infinite number of solutions
4) Inconsistent ­­> No solution
Algebra I
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Chp. 6.1 ­ Graphing Systems of Equations
March 19, 2013
Examples:
Ex. 1 ­ Classify the system of equations as consistent or inconsistent, dependent or independent.
a) y = 2x + 3
b) y = ­2x + 3
y = ­2x ­ 5
y = ­2x ­ 5
c) y = 3x + 5
y = 3x + 5
Ex. 2 ­ Graph each system and determine the number of solutions. If it has a solution, state it.
10
a) x ­ y = 2
8
3y + 2x = 9
6
4
2
­10
­8
­6
­4
­2
2
4
6
8
10
2
4
6
8
10
2
4
6
8
10
­2
­4
­6
­8
­10
10
b) y = ­2x ­ 3
8
6x + 3y = ­9
6
4
2
­10
­8
­6
­4
­2
­2
­4
­6
­8
­10
10
c) 2x ­ y = ­1
8
4x ­ 2y = 6
6
4
2
­10
­8
­6
­4
­2
­2
­4
­6
­8
­10
Algebra I
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Chp. 6.1 ­ Graphing Systems of Equations
March 19, 2013
Homework:
p. 336 (#10­24)
Algebra I
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