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)

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

Remember: Why does it happen?

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 and solve for the other variable 0): THINK: Which variable is easiest to use 5): Check

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 equations substitute and solve for the other variable 0): THINK: Which variable is easiest to use 5): Check

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.

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

CONCEPT SUMMARY: METHODWHEN TO USE SubstitutionWhen one equation is already solved: y=mx+b or x= ym+b. =A AB-4AD E75638D0

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 d=02B482AE-EB9F-4960-BC5C-7D2360BDEE66

ADDITIONALLY: System of equations help us solve real world problems. cfm?guidAssetId=A AB-4AD E75638D0 VIDEO-Word Prob.

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

GOAL:

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?

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

SOLUTION: (Continue) 2) Solve the system of equations for the break-even point using the best method. $0.80x = $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.

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?

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

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.

CLASSWORK: Page Problems: 2, 4, 6, 7, 10, 12, 14, 15, 16.