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6.4 Application of Linear SystemsI can choose the best method for solving a system of linear equations
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When to Use Graphing: When you want a visual display of the equations,
or when you want to estimate a solution.
Substitution: When one equation is already solved for one of the variables, or when it is easy to solve for one of the variables.
Elimination: When the coefficients of one variable are the same or opposites, or when it is not convenient to use graphing or substitution.
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Modeling Problems A break-even point is where a business’ expenses equal its
income
Ex:
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Practice A fashion designer makes and sells hats. The material for
each hat costs $5.50 and the hats sell for $12.50 each. If the designer spends $1400 on advertising, how many hats must be sold for the designer to break even?
Let x = # of hats and y = amount of money Expenses: y = 5.50x + 1400 Income: y = 12.50x
Use substitution: 12.50x = 5.50x +1400 7x = 1400 x = 200
After selling 200 hats
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Constraints and Viable Solutions The local zoo is filling two water tanks for the elephant exhibit. One has
50 gallons in it and is being filled at a rate of 10 gal/h while the other has 29 gallons and is being filled at a rate of 3 gal/h when will they have the same amount?
Let x = # of hours and y = # of gallons 1st tank: y = 10x + 50 2nd tank: y = 3x + 29
Substitute: 10x + 50 = 3x + 29 7x = -21 x = -3
Since x is the number of hours and the solution is negative, we know the tanks will never have the same amount.
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Wind or Current
Tailwind: air speed + wind speed = ground speed Headwind: air speed – wind speed = ground speed
Ex:
LA to Charlotte: a + w = 550 Charlotte to LA: a – w = 495 Use Elimination: 2a = 1045 a = 522.5 mi/h Plug a in to find w = 27.5 mi/h
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Assignment P.390 odds #7-25