1. Bellwork Solve using any method.
1.) 3x + 2y =26
x + y = 7
2.) -4x - 4y = 16
4x + 5y = 14

2. 6-4 Applications of Linear Systems
Algebra 1

3. Ways to solve a system of linear equations
Graphing – a visual model
Substitution – A useful method when one of the variables has a coefficient of 1 or -1.
Elimination– A useful method when none of the variables has a coefficient of 1 or -1.

4. Choosing a solution method
Example 1-
2x + y = 0
x + y = 5

5. Choosing a solution method
Example 2 –
3x + 5y = 25
2x – 6y = 12

6. Setting up a word problem
Usually has one equation like
x + y = ___ representing a # .
The other equation looks like
__x + __y = ____ which could represent $ or weight or …
The a, b represent numbers given within the problem.

7. Word problems
Ex. 3 – A health food store mixes granola that costs them $4 per pound and raisins that cost them $2 per pound together to make 25 pounds of raisin granola. How many pounds of raisins should they include if they want the mixture to cost them a total of $80?

8. Break even (same, equal) Word problems
Ex. 4
Printing a newsletter costs $1.50 per copy plus $450 in printer’s fees. The copies are sold for $3 each. How many copies of the newsletter must be sold to break even?

9. Solving a wind or current problem
x + y = ___ (mi/hr or rate) with wind or current
x – y = ___ (mi/hr or rate) against wind or current

10. Ex. 5
A traveler is walking on a moving walkway in an airport. The traveler must walk back on the walkway to get to the gate. The traveler’s groundspeed is 2 ft/s against the walkway and 6 ft/s with the walkway. What is the traveler’s speed off the walkway? What is the speed of the moving walkway?

11. ASSIGNMENT

12. Word problems
Ex. 4 – You are offered two different credit cards. Card A charges $75 per year and 15% interest on your average balance. Card B charges $15 per year and 18% interest on your average balance. What would your average balance need to be for the cards to cost you the same amount?