6.4 Application of Linear SystemsI can choose the best method for solving a system of linear equations

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.

Modeling Problems A break-even point is where a business’ expenses equal its

income

Ex:

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

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.

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

Assignment P.390 odds #7-25