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Linear Models and Systems
Unit 2Advance 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
Write the Explicit formula.
0
1
5
7 where 1n n
U
U U n
Consider the recursively defined arithmetic sequence.
a. Find an explicit formula for the sequence.b. Use the explicit formula to find .c. Find the value of n so that .
0
1
13
-3 where 1n n
U
U U n
17U50nU
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
equationDependent variable, Independent variable, Domain, Range.
• Convert the following linear equation to intercept form:
5 3 6
2 4 8
5 4 20
x y
x y
y x
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. 2HW 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 Consistent Dependent Independent
• Warm-UpFactor: 216 8 1x x
Substitution
Elimination
• Solve the system by elimination.
Elimination
• Solve the system by elimination.
Advance Algebra Oct. 3
Objectives:
• Warm-upGraph the following 3 equations:
3
4
2 3 3
y
x y
x y
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-UpGraph the 3 linear inequalities and shade in the area that overlap.
1y
4 2 6x y
4 2 6x y
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 ay 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-UpFactor the following.
3 2
2
a. 6 15 21
b. 3 28
x x x
x x
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.
3x y
Graph the Inequality.
3x y
x y
Graph the Inequality.
3x y
x y
0.5y
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:
2 7
7 14 21
5 3 17
y x
y x
x y
• To use the graphing calculator a linear equation has to be in “y=“ form. Graph the following on your calculator:
2 7
7 14 21
5 3 17
y x
y x
x y
• To use the graphing calculator a linear equation has to be in “y=“ form. Graph the following on your calculator:
2 7
7 14 21
5 3 17
y x
y x
x y
• To use the graphing calculator a linear equation has to be in “y=“ form. Graph the following on your calculator:
2 7
7 14 21
5 3 17
y x
y x
x y
• Now Graph the following Linear Inequalities:Prob. 5, page 357
0.51 5
1.6 8
0.1 2
0
0
y x
y x
y x
y
x
• Now Graph the following Linear Inequalities:
0.51 5
1.6 8
0.1 2
0
0
y x
y x
y x
y
x
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.
2 8
4
2
x y z
y z
x y z
Example B: Solving systems with 3 variables.
2 1
4
2
x y z
y z
x y z
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. 3Graph this system of inequalities , label the vertices of the feasible region. And name the integer coordinates the maximize the function
5,500
5,000
3
40,000
x
y
y x
x y
0.08 0.10P x y
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-UpUse technology and the inverse matrix method to solve this system
2 2 5
6 2 4 3
4 3 5
x y z
x y z
x y z
1 1
1
1
A X B
A A X A B
I X A B
X A B
October 15, 2014
Objectives:1. Students will demonstrate understanding of
Linear Systems by use of: (Unit Test)a. Mathematical modelsb. Equations and Inequalitiesc. Tablesd. Written explination
October 17, 2014
