chapter 6 solving systems of equations and inequalities
DESCRIPTION
Chapter 6 solving systems of equations and inequalities. 6.1 solve linear systems by graphing. Systems of linear equations. System of Linear Equations – two or more linear equations to be solved at the same time EX: 6x + 5y = 290 x + y = 50 - PowerPoint PPT PresentationTRANSCRIPT
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CHAPTER 6SOLVING SYSTEMS
OF EQUATIONS AND INEQUALITIES
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6.1SOLVE LINEAR
SYSTEMS BY GRAPHING
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System of Linear Equations – __________________ linear equations to be _______________ at the __________________
EX:
Solution of a System of Linear Equations – an _____________ ________________ that satisfies _________________________ in the system.
EX:
SYSTEMS OF LINEAR EQUATIONS
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1) Graph ____________ equations in the __________________ _________________________________. Use ___________________________ form. Use your slope to go up and over
_______________________________.
2) The ___________________ where the two lines ___________ in the _______________.
METHOD 1: SOLVING BY GRAPHING
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x – y = 53x + y = 3
EX: SOLVE THE LINEAR SYSTEM BY GRAPHING.
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2x + y = -3-6x + 3y = 3
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6.2SOLVE LINEAR
SYSTEMS BY SUBSTITUTION
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1) Solve ___________ of the equations for ________________ ______________________. Pick the variable that is
_____________________________________.
2) __________________ the expression from _______________ into the _____________________ and _____________________ ___________________________________.
3) _________________ the value from ______________ into _____________________of the equations and ______________ for the ________________________________.
METHOD 2: SOLVING BY SUBSTITUTION
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y = 2x + 53x + y = 10
3x + y = -7-2x + 4y = 0
x + y = -2-8x - y = 4
NOTEBOOK EXAMPLE #1: SOLVE USING SUBSTITUTION.
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Kara spends $16 on tubes of paint and disposable brushes for an art project. Each tube of paint costs $3 and each disposable brush costs $0.50. Kara purchases twice as many brushes as tubes of paint. Find the number of each that she bought.
EX:
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A chemist needs 15 liters of a 60% alcohol solution. The chemist has a solution that is 50% alcohol. How many liters of the 50% alcohol solution and pure alcohol should the chemist mix together to make 15 liters of a 60% alcohol solution?
EX:
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6.3SOLVE LINEAR
SYSTEMS BY ADDING OR SUBTRACTING
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1) ________________________ the equations to ____________ one variable. Make sure ______________________are ____________________.
2) Solve the ____________________ for the ________________ variable.
3) ______________________ the value from ______________ into ________________________________ and ____________ for the ___________________________.
METHOD 3: SOLVING BY ELIMINATION
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4x – 3y = 5-2x + 3y = -7
7x – 2y = 57x – 3y = 4
3x + 4y = -62y = 3x + 6
NOTEBOOK EXAMPLE #2: SOLVE BY ELIMINATION
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During a kayak trip, a kayaker travels 12 miles upstream (against the current) in 3 hours and 12 miles downstream (with the current) in 2 hours. The speed of the kayak remained constant throughout the trip. Find the speed of the kayak in still water and the speed of the current.
http://www.physicsclassroom.com/mmedia/vectors/plane.cfm
EX:
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A business center charges a flat fee to send faxes plus a fee per page. You send one fax with 4 pages for $5.36 and another fax with 7 pages for $7.88. Find the flat fee and the cost per page.
EX:
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6.4SOLVE LINEAR
SYSTEMS BY MULTIPLYING FIRST
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Sometimes you may have to _____________________ one or both equations by a _________________ to create _____________________ that are ___________________ of each other.
Doing this will allow you to ____________________ a variable when the equations are ___________________.
METHOD 3: SOLVING BY ELIMINATION
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2x + 5y = 33x + 10y = -3
8x – 5y = 114x – 3y = 5
3x – 7y = 59y = 5x + 5
NOTEBOOK EXAMPLE #3:SOLVE BY ELIMINATION
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Dunham’s is having a sale on soccer balls. A soccer coach purchases 10 soccer balls and 2 soccer ball bags for $155. Another coach purchases 12 soccer balls and 3 soccer ball bags for $189. Find the cost of a soccer ball and the cost of a soccer ball bag.
EX:
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6.5SOLVE SPECIAL
TYPES OF LINEAR SYSTEMS
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A system of equations has _____________________ if the lines are ______________________.
Same ________________.
Different ___________________.
Called an ___________________ ____________________________.
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A system of equations has _____________________________ solutions if the lines are _______________________________.
Same ______________________.
Same ______________________.
Called a _________________________ ______________________________
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A system of equations has ______________________ if the lines ____________________________________________.
Different _____________________.
Called _______________________ _____________________________
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SUMMARY:
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5x + 3y = 615x + 9y = 8
y = 2x – 4-6x + 3y = -12
3x – 2y = -54x + 5y = 47
NOTEBOOK EXAMPLE #4 SOLVE THE SYSTEM USING
SUBSTITUTION OR ELIMINATION.
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Without solving the linear system, tell whether it has one solution, no solution, or infinitely many solutions.
5x + y = -2-10x – 2y = 4
6x + 2y = 36x + 2y = -5
NOTEBOOK EXAMPLE #5
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A pizza parlor fills two pizza orders. Is there enough information to determine the cost of one medium pizza?
EX:
Medium Large Cost4 12 $1688 24 $336
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