Chapter 8 – Systems of Non-Linear Equations

7 Days

8.1 Systems of Equations

Two days

Solving Systems of Equations

12

42

xy

xy

Solving Systems of Equations

7

1022

yx

yx

p590 #2,5,11,13,19 - 21, 26 NO TI

Homework

Solving Systems

25

252

22

yx

yx

Solving Systems with the TI

0yx2

922 yx

p590 #15, 18,25,26,48,50,52

Homework

11-1 WS #5-20all, 23,25

Homework

8.3 Systems of Inequalities

Two days

Graphing systems of inequalities

22

42

xy

xy

Graphing systems of inequalities

54

252

22

xxy

yx

Graphing systems of inequalities

34

9122

22

xxy

yx

pg 608 #5-11 odd, 15, 19, 23-29 odd

Homework

pg 608 #6-10 even, 16, 22-32 even

Homework

Field Trip: LD is preparing a trip to New York for 400 students. The company who is providing the transportation has small buses of 40 seats each and large buses of 50 seats, but only has 9 drivers available. Graph the system of inequalities to show all possible combinations of small buses and large buses that could be used for the trip.

Deal at the Outlets: Aeropostale at the Outlets in Hershey wants to liquidate 200 of its shirts and 100 pairs of pants from last season. They have decided to put together two offers, A and B. Offer A is a package of one shirt and a pair of pants]. Offer B is a package of three shirts and a pair of pants. The store does not want to sell less than 20 packages of Offer A and no less than 10 of Offer B. Graph the system of inequalities to show all possible combination of offer A and offer B that can be sold.

pg 610 #35-38, 41

Homework

Chicken Feed: One of your friends who owns a local farm asks you to use mathematics to help them save money. They have their chickens a healthy diet to gain weight. The chickens have to consume at least 15g of grain and at least 15g of protein. In the local market there are only two types of chicken feed for sale: Type X, with a composition of one gram of grain to five grams of protein, and another type, Y, with a composition of five grams of grain to one gram of protein. The price of a bag of Type X is $10 and Type Y is $30. What are the quantities of each type of feed that have to be purchased to cover the needs of the diet with a minimal cost?

Systems of Inequalities WS

Homework

8.5 MatricesFour Days

Inverses can be used to solve systems of equations. Solving large systems requires a different method using an augmented matrix.

An augmented matrix consists of the coefficients and constant terms of a system of linear equations.

A vertical line separates the coefficients from the constants.

To write an augmented matrix, be sure your equations are in the form ax + by = c or ax + by + cx = d.

Write the augmented matrix for the system of equations.

Write the augmented matrix.

You can use the augmented matrix of a system to solve the system. First you will do a row operation to change the form of the matrix. These row operations create a matrix equivalent to the original matrix. So the new matrix represents a system equivalent to the original system.

For each matrix, the following row operations produce a matrix of an equivalent system.

Row reduction is the process of performing elementary row operations on an augmented matrix to solve a system. The goal is to get the coefficients to reduce to the identity matrix on the left side.This is called reduced row-echelon form.

1x = 5

1y = 2

Solving Systems of 2 Equations and 2 Unknowns

33

82

yx

yx

Solving Systems of 3 Equations and 3 Unknowns

243

342

432

zyx

zyx

zyx

Homework

8.5 Matrices Day 2

Get into groups of 4 students and solve the following systems using matrices.

Warm-up

723

922

63

zyx

zyx

zyx

1022

632

853

zyx

zyx

zyx

Pg 633 (#1, 3, 19)

Homework

8.5 Matrices Day 3

Warm-up #1

1935

682

yx

yx

Warm-up #2

4336

32

533

zyx

zyx

zyx

Challenge!

6.2834

9.24103

5.342

123

4321

4321

4321

4321

xxxx

xxxx

xxxx

xxxx

pg 633 (# 2, 4, 18, 20)

Homework

Pg 633 (# 5,10 by hand; 7,8 w/ calc) Pg 673 (# 9,10,16 w/ calc)

Homework

8.6 Operations on Matrices

2 Days

The size of a matrix is #Rows x #Columns

Size of a Matrix

Matrices to be added must the same size.

Adding and Subtracting Martices

Scalar Multiplication - each element in a matrix is multiplied by a constant.

1. 2 7 1 0 -14 2 0

2. 4 2 0

4 5

-8 0

16 -20

3. 5

1 2 3

4 5 6

7 8 9

-5 -10 15

-20 25 -30

35 -40 45

Matrix Multiplication

**Multiply rows times columns.**You can only multiply if the number of columns in the 1st matrix is equal to the number of rows in the 2nd matrix.

3 2 5

7 1 0

8 2

1 5

0 3

Dimensions: 3 x 22 x 3

They must match.

The dimensions of your answer.

Examples:

1. 2 1

3 4

3 9 2

5 7 6

2(3) + -1(5)

2(-9) + -1(7) 2(2) + -1(-6)

3(3) + 4(5) 3(-9) + 4(7) 3(2) + 4(-6)

1 25 10

29 1 18

3 9 2 2 1.

5 7 6 3 4

2

Dimensions: 2 x 3 2 x 2

*They don’t match so can’t be multiplied together.*

1 2 1 1

1 3 2 7

2 6 1 8

x

y

z

3.

x 2y z 1

x 3y 2z 7

2x 6y z 8

0 1 4 3

1 0 2 5

4.

2 x 2 2 x 2

*Answer should be a 2 x 2

0(4) + (-1)(-2) 0(-3) + (-1)(5)

1(4) + 0(-2)

1(-3) +0(5)

2 -5

4 -3

Matrix Practice

43

21

31

23

BA

BA Find

AB Find

??? Does ABBA

More Practice

10

01

34

22

BA

BA Find

AB Find

10

01 :MatrixIdentity

I

AAI

AIA

:Matrices ofProperty Identity