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

6-4 Applications of Linear Systems Algebra 1

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.

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

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

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.

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?

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?

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

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?

ASSIGNMENT

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?