Objective: To be able to solve linear systems graphicallyPOD Graph the following piecewise function

1 3, if 2 2

( ) 2, if 2 11, if 1

x x

f x x xx

Try another one for practice

2 4, if 2 3

( ) 3, if 2 23 4, if 22

x x

f x x

x x

Problem: The chex snack company would like to market a new snack that will contain nuts and dried fruit. The cost of a lb of nuts is $1 and the cost of a lb of dried fruit is $2. The company would like to keep the cost of the bag at $4, and at the same time the amount of nuts in the mixture should be 2 times as many as the dried fruit for optimal taste.

Question: How many lbs of dried fruits and how many lbs of nuts should be used in each bag?

A problem like this involves a system(2 equations acting on the same variables)Let y represent the lbs of nuts in the mixtureLet x represent the lbs of dried fruit in the mixture

Write an equation that related the numbers of lbs of nuts and dried fruit that can be bagged for $4

Write an equation that related the numbers of lbs of nuts and dried fruit to represent the taste preference

1) The Cost

2) The Taste

NUTS(y)

DRIED FRUIT(x)

HOW MANY LBS NUTS AND HOW MANY LBS FRUIT SHOULD BE USED IN THE MIX?

Ex. 1 Solve the system Ex. 2 Try this one

Ex. 3 Solve the system Ex. 4 Solve the system

Types of situations in solving linear systemsEx. 5 Solve the system2x + 3y = 64x + 6y = 12

Ex. 6 Solve the system2x + y = 42x + y = 1

Graphing Systems Results in The following Situations

Number of Solutions Number of Solutions Number of Solutions

Ex. 7 Ex. 8

Ex. 9 Solve the systemy = 3 + 4x20x - 5y = -15