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REVIEW: 6.1 Solving by Graphing:

Remember:. To graph a line we use the slope intercept form:. REVIEW: 6.1 Solving by Graphing:. y = m x + b. Slope = = . STARING POINT (The point where it crosses the y-axis). System Solution : The point where the two lines intersect (cross):. (1, 3).

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REVIEW: 6.1 Solving by Graphing:

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

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

  3. Remember: What are the requirements for this to happen?

  4. 0): THINK- Which variable is the easiest to isolate? 1): Isolate a variable REVIEW: 6.2: Solving by Substitution: 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 5): Check

  5. 0): THINK: Which variable is easiest to eliminate. 1): Pick a variable to eliminate 6.3: Solving by Elimination: 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. 5): Check

  6. 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.

  7. CONCEPT SUMMARY: http://player.discoveryeducation.com/index.cfm?guidAssetId=8A6198F2-B782-4C69-8F6D-8CD683CAF9DD&blnFromSearch=1&productcode=US

  8. YOU TRY IT: Solve the system by Graphing:

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

  10. CONCEPT SUMMARY: http://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/fast-systems-of-equations/v/solving-linear-systems-by-substitution?exid=systems_of_equations http://player.discoveryeducation.com/index.cfm?guidAssetId=A9199767-40AB-4AD1-9493-9391E75638D0

  11. YOU TRY IT: Solve the system by Substitution:

  12. YOU TRY IT:(SOLUTION)  x = 1

  13. CONCEPT SUMMARY: (continue) http://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/fast-systems-of-equations/v/solving-systems-of-equations-by-elimination http://player.discoveryeducation.com/index.cfm?guidAssetId=02B482AE-EB9F-4960-BC5C-7D2360BDEE66

  14. YOU TRY IT: Solve the system by Elimination:

  15. YOU TRY IT: (SOLUTION) +  x = 1 10  y = 4

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

  17. 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.

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

  19. GOAL:

  20. 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?

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

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

  23. 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?

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

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

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

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

  28. SUMMARY: http://www.bing.com/videos/search?q=SYSTEM+OF+EQUATIONS+&view=detail&mid=2CFE63B47EDB353AFDCF2CFE63B47EDB353AFDCF&first=0&FORM=NVPFVR

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