linear models and systems unit 2 advance algebra
TRANSCRIPT
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Linear Models and Systems
Unit 2Advance Algebra
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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.
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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?
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September 19 Objectives
• Write explicit formulas for arithmetic sequences.
• Write linear equations in intercept form.
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Notes:Recursive formula
Write the Explicit formula.
0
1
5
7 where 1n n
U
U U n
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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
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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.
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• Convert the following linear equation to intercept form:
5 3 6
2 4 8
5 4 20
x y
x y
y x
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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
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Point-Slope form.
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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.
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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
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Warm-Up
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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
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• Warm-UpFactor: 216 8 1x x
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Substitution
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Elimination
• Solve the system by elimination.
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Elimination
• Solve the system by elimination.
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Advance Algebra Oct. 3
Objectives:
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• Warm-upGraph the following 3 equations:
3
4
2 3 3
y
x y
x y
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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.
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• Warm-UpGraph the 3 linear inequalities and shade in the area that overlap.
1y
4 2 6x y
4 2 6x y
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Describe what is happening with each step.
ax by c
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ax by c
by c ax
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ax by c by c ax by c ax
b b b
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ax by c
by c ax by c ax
b b b
c ay x
b b
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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
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Warm-UpFactor the following.
3 2
2
a. 6 15 21
b. 3 28
x x x
x x
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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.
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Graph the Inequality.
3x y
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Graph the Inequality.
3x y
x y
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Graph the Inequality.
3x y
x y
0.5y
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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.
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• 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
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• 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
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• 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
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• 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
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• 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
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• 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
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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.
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Example A: Solving systems with 3 variables.
2 8
4
2
x y z
y z
x y z
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Example B: Solving systems with 3 variables.
2 1
4
2
x y z
y z
x y z
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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.
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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
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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.
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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
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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
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October 17, 2014
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