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REVIEW: 6.1 Solving by Graphing: Remember: To graph a line we use the slope intercept form: y = mx +b STARING POINT (The point where it crosses the y-axis)

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System Solution: The point where the two lines intersect (cross): (1, 3)

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Remember: What are the requirements for this to happen?

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REVIEW: 6.2: Solving by Substitution: 1): Isolate a variable 2): Substitute the variable into the other equation 3): Solve for the variable 4): Go back to the original equations, substitute, solve for the second variable 0): THINK - Which variable is the easiest to isolate? 5): Check

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6.3: Solving by Elimination: 1): Pick a variable to eliminate 2): Add the two equations to Eliminate a variable 3): Solve for the remaining variable 4): Go back to the original equation, substitute, solve for the second variable. 0): THINK: Which variable is easiest to eliminate. 5): Check

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NOTE: We can solve system of equations using a graph, the substitution or eliminations process. The best method to use will depend on the form of the equations and how precise we want the answer to be.

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CONCEPT SUMMARY: METHODWHEN TO USE GraphingWhen you want a visual display of the equations, or when you want to estimate the solution. http://player.discoveryeducation.com/index.cfm?guidAs setId=8A6198F2-B782-4C69-8F6D- 8CD683CAF9DD&blnFromSearch=1&productcode=US

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YOU TRY IT: Solve the system by Graphing:

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YOU TRY IT: (SOLUTION) (1,4)

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CONCEPT SUMMARY: METHODWHEN TO USE SubstitutionWhen one equation is already solved: y=mx+b or x= ym+b. http://player.discoveryeducation.com/index.cfm?guidAssetId=A9199767-40AB-4AD1-9493-9391E75638D0 http://www.khanacademy.org/mat h/algebra/systems-of-eq-and- ineq/fast-systems-of- equations/v/solving-linear- systems-by- substitution?exid=systems_of_equ ations

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YOU TRY IT: Solve the system by Substitution:

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YOU TRY IT:(SOLUTION)

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CONCEPT SUMMARY: (continue) METHODWHEN TO USE EliminationWhen the equations are in Ax +By = C form or the coefficients of one variable are the same and/or opposites http://player.discoveryeducation.com/index.cfm?guidAssetId=02B482AE-EB9F-4960-BC5C- 7D2360BDEE66 http://www.khanacademy.org/mat h/algebra/systems-of-eq-and- ineq/fast-systems-of- equations/v/solving-systems-of- equations-by-elimination

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YOU TRY IT: Solve the system by Elimination:

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YOU TRY IT: (SOLUTION) x = 1 + y = 4

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ADDITIONALLY: System of equations help us solve real world problems. http://player.discoveryeducation.com/index. cfm?guidAssetId=A9199767-40AB-4AD1- 9493-9391E75638D0 VIDEO-Word Prob.

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NOTE: We can solve system of equations using a graph, the substitution or eliminations process. The best method to use will depend on the form of the equations and how precise we want the answer to be.

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6.4 Application of Linear Systems: Break-Even Point: The point for business is where the income equals the expenses.

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GOAL:

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MODELING PROBLEMS: Systems of equations are useful to for solving and modeling problems that involve mixtures, rates and Break-Even points. Ex: A puzzle expert wrote a new sudoku puzzle book. His initial costs are $864. Binding and packaging each book costs $0.80. The price of the book is $2.00. How many books must be sold to break even?

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SOLUTION: 1) Write the system of equations described in the problem. Income: y = $2x Let x = number of books sold Let y = number of dollars of expense or income Expense: y = $0.80x + 864

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SOLUTION: (Continue) 2) Solve the system of equations for the break-even point using the best method. $0.80x + 864 = $2x To break even we want: Expense = Income 864 = 2x -0.80x 864 = 1.2x 720 = x There should be 720 books sold for the puzzle expert to break-even.

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YOU TRY IT: Ex: A fashion designer makes and sells hats. The material for each hat costs $5.50. The hats sell for $12.50 each. The designer spends $1400 on advertising. How many hats must the designer sell to break-even?

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SOLUTION: 1) Write the system of equations described in the problem. Income: y = $12.50x Let x = number of hats sold Let y = number of dollars of expense or income Expense: y = $5.50x + $1400

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SOLUTION: (Continue) 2) Solve the system of equations for the break-even point using the best method. $5.50x + $1400 = $12.50x To break even we want: Expense = Income 1400 = 12.5x -5.50x 1400 = 7x 200 = x There should be 200 hats sold for the fashion designer to break-even.

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VIDEOS: Special Linear Equations https://www.khanacademy.org/math/algebra/syst ems-of-eq-and-ineq/fast-systems-of- equations/v/special-types-of-linear-systems

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CLASSWORK: Page 386-388 Problems: As many as needed to master the concept.

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SUMMARY: http://www.bing.com/ videos/search?q=SYSTE M+OF+EQUATIONS+&v iew=detail&mid=2CFE6 3B47EDB353AFDCF2CF E63B47EDB353AFDCF& first=0&FORM=NVPFVR

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Lesson 4-2: Solving Systems – Substitution & Linear Combinations Objectives: Students will: Solve systems of equations using substitution and linear combinations.

Lesson 4-2: Solving Systems – Substitution & Linear Combinations Objectives: Students will: Solve systems of equations using substitution and linear combinations.

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