1. 6.4 Application of Linear Systems
I can choose the best method for solving a system of linear equations

2. 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.

3. Modeling Problems
A break-even point is where a business’ expenses equal its income
Ex:

4. 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
Income: y = 12.50x
Use substitution: 12.50x = 5.50x +1400
7x = 1400
x = 200
After selling 200 hats

5. 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.

6. 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 = mi/h
Plug a in to find w = 27.5 mi/h

7. Assignment
P.390 odds #7-25