Linear Models and Systems
Unit 2
Advance Algebra
Objectives Sep. 17-18
• Identify and algebraically transform systems of
linear equations.
• Define what it means to solve a system of
equations.
• Make connections between linear equations
and arithmetic sequences.
Group work – 2 person, present on white board.
• The senior class hosted a spaghetti dinner to
raise money for the local animal shelter.
• They sold CHILD tickets for $8 each and ADULT
tickets for $12 each.
• Altogether they sold 137 tickets and they
made a total of $1472 for the animal shelter.
•
How many tickets of each type were sold?
September 19 Objectives
• Write explicit formulas for arithmetic
sequences.
• Write linear equations in intercept
form.
Page 126
Notes:
Recursive formula
U0  5
U n U n 1  7 where n  1
Write the Explicit formula.
Consider the recursively defined arithmetic
sequence.
U 0  13
U n U n 1 -3 where n  1
a. Find an explicit formula for the sequence.
b. Use the explicit formula to find U17 .
c. Find the value of n so that U  50 .
n
September 22, 2014
Objectives:
1. Given two points on a graph determine the
slope.
2. Convert a linear equation to Intercept form.
3. Use academic language to describe a linear
equation
Dependent variable, Independent variable,
Domain, Range.
• Convert the following linear equation to
intercept form:
5x  3 y  6
2 x  4 y  8
5 y  4 x  20
September 24-25
Objectives:
1. Determine how to estimate a Line of Fit given
a set of data.
2. Given the slope and one point of a line use
the Point-Slope form to write a linear
equation.
Line of Fit Interpolation Extrapolation
Point-Slope form
Point-Slope form.
September 29, 2014
Objectives:
1. Explain what is meant by a System of
equations.
2. Given a set of data that represents a system
of equation; find the solution.
System of equations, Solution to a system of
equations.
September 30, 2014
Objectives:
1. Given a system of linear equations use
substitution to find the solution.
Reminder:
Unit 1 Portfolios are due Oct. 2
HW 3D ; page 164 1-7 and page 170 1-4 due Oct.
3
Warm-Up
October 1, 2014
Objectives:
1. Solve a system of linear equations using
substitution and elimination.
2. Classify system of equations as a think
pair share activity.
Inconsistent
Independent
Consistent
Dependent
• Warm-Up
2
Factor:
16 x
 8x  1
Substitution
Elimination
• Solve the system by elimination.
Elimination
• Solve the system by elimination.
Advance Algebra Oct. 3
Objectives:
• Warm-up
Graph the following 3 equations:
y3
x y 4
2 x  3 y   3
October 6, 2014
Objectives.
1. Students will analyze the work of other
students and critique / grade the work for
solving a system of linear equations.
2. Students will graph the appropriate region of
a linear inequality.
• Warm-Up
Graph the 3 linear inequalities and shade in the
area that overlap.
y  1
4x  2 y  6
4 x  2 y  6
Describe what is happening with each step.
ax  by  c
ax  by  c
by  c  ax
ax  by  c
by  c  ax
by c ax
 
b b b
ax  by  c
by  c  ax
by c ax
 
b b b
c a
y  x
b b
October 7, 2014
Objectives:
1. Students will graph linear inequalities and
use a test point to check for correctness.
2. Students will be able to identify the feasible
region of linear inequalities and describe this
region in terms of constraints.
Constraints
Vertex
Feasible Region
Warm-Up
Factor the following.
a.
6 x  15 x  21x
3
2
b. x  3x  28
2
Rachel has 3 hours to work on her
homework tonight. She wants to spend
more time working on math than on
chemistry, and she must spend at least a half
hour working on chemistry.
Let x = time in hours spent on math.
Let y = time in hours spent on chemistry.
Write inequalities to represent the three
constraints of the system.
Graph the Inequality.
x y3
Graph the Inequality.
x y3
x y
Graph the Inequality.
x y3
x y
y  0.5
October 9, 2014
Objectives:
1. Students will describe the procedure on
creating a system of inequalities.
2. Use technology to graph inequalities.
3. Students will use an algebraic method to
determine the solution of a 3 variable
system.
• Warm-Up: To use the graphing calculator a
linear equation has to be in “y=“ form. Graph
the following on your calculator:
y  2x  7
7 y  14 x  21
5 x  3 y  17
• To use the graphing calculator a linear
equation has to be in “y=“ form. Graph the
following on your calculator:
y  2x  7
7 y  14 x  21
5 x  3 y  17
• To use the graphing calculator a linear
equation has to be in “y=“ form. Graph the
following on your calculator:
y  2x  7
7 y  14 x  21
5 x  3 y  17
• To use the graphing calculator a linear
equation has to be in “y=“ form. Graph the
following on your calculator:
y  2x  7
7 y  14 x  21
5 x  3 y  17
• Now Graph the following Linear Inequalities:
Prob. 5, page 357
y  0.51x  5
y  1.6 x  8
y  0.1x  2
y0
x0
• Now Graph the following Linear Inequalities:
y  0.51x  5
y  1.6 x  8
y  0.1x  2
y0
x0
October 10, 2014
• Objectives:
1. Given a situation with multiple constraints
the student will develop a system of
inequalities.
2. Identify the vertex points of a feasible region
and determine if they are a maximum or
minimum point.
Example A: Solving systems with 3 variables.
x  2y  z  8
yz4
x yz2
Example B: Solving systems with 3 variables.
x  2y  z 1
yz4
x  y  z  2
Oct. 13, 2014
Objectives:
1. Organize information in a table and construct
inequalities of the constraints.
2. Analyze the maximum or minimum of a
system of inequalities.
Page 363, prob. 3
Graph this system of inequalities , label the
vertices of the feasible region. And name the
integer coordinates the maximize the function
P  0.08 x  0.10 y
x  5,500
y  5,000
y  3x
x  y  40,000
October 14, 2014
Objectives:
1. Students will optimize a system of
inequalities by finding the maximum profit.
2. Students will restate the solution of a system
linear programing in the context of the
problem.
Warm-Up
Use technology and the inverse matrix method
to solve this system
A X    B 

2x  y  2z  5
1
1
 A  A X    A  B 
6x  2 y  4z  3
1
 I  X    A  B 
4 x  y  3z  5
1
 X    A  B 
October 15, 2014
Objectives:
1. Students will demonstrate understanding of
Linear Systems by use of: (Unit Test)
a. Mathematical models
b. Equations and Inequalities
c. Tables
d. Written explination
October 17, 2014