Transcript Inequalities With Linear Systems

Vocabulary
1.
2.
3.
4.
5.
6.
7.
8.
Linear
Inequality
Variable
Greater Than
Less Than
Equal To
Substitution
Method
Number Line
9.
10.
11.
12.
13.
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15.
16.
Symbol
Solution
17.
Equation
18.
Fraction
19.
Decimal
Point of
Intersection 20.
Linear System
Combination
Method
Geometry
Algebra
Problem
Solving
Strategies
Midpoint
Symbols
Greater Than
Less Than
Equal To
Greater Than or Equal To
Less Than or Equal To
>
<
=
>
<
Using a Number Line
3X + 4 < 13
0 What numbers satisfy this equation?
3X + 4 < 13
-What numbers satisfy this equation?
Number Line Solving
1. 3x + 12 = 5x -4
9. 14x -23 < 5x + 13
2. 3w + 12 < 5w -4
10. 3,975 + 6d < 995 + 17.95d
3. q- 5 = 6q + 10
4. r – 5 > 6r + 10
5. 3x + 17 < 47
6. -6x +9 < 25
7. 18 < -4X +2
8. 43 < 8X -9
Point of Intersection
0 Where two lines meet/touch/cross
0 Found using the 6 Step Method
0 Found using the Substitution Method
0 Found using the Combination Method
Problem Solving Strategies
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6.
Make A Table
Draw a Picture
Solve a Simpler Problem
Make an Equation
Work Backwards
Guess and Check
6 Step Method
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6.
Set Equations Equal
Get All X’s on One Side
Get All Numbers on One Side
X=?
Substitute X Back Into One Equation
Point of Intersection
Problem 2.1
1. What kinds of equations will show how the costs for
the two companies are a function of the number of
days?
2. What pattern do you expect to see in graphs of the
equations?
3. How can you use a graph to answer the questions
about which company offers the best price?
2.1 Continued
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5.
For what number of days will the costs for the two
companies be the same? What is that cost?
For what numbers of days will Super Locks cost less
than Fail Safe?
For what numbers of days will Super Locks cost less
than $6000?
What is the cost of one year of service from Fail Safe?
How can Fail Safe adjust its per-day charge to make its
cost for 500 days of service cheaper than Super Locks’
cost?
2.1 Continued
B. For each company, write an equation for the cost c for
days d of security services.
Problem 2.2
C = 3,975 + 6d (Super Locks)
C= 995 + 17.95d (Fail Safe)
Find Point of Intersection:
1. Using 6 Step Substitution Method
2. Using Combination Method
Applications Pg. 30
0 Sam needs to rent a car for a one-week trip in Oregon. He is
considering two companies. A+ Auto Rental charges $175
plus $0.10 per mile. Zippy Auto Rental charges $220 plus
$0.05 per mile.
a.
b.
c.
d.
e.
Write an equation relating the rental cost for each company
to the miles driven.
Graph the equations
Under what circumstances is the rental cost the same for
both companies? What is that cost?
Under what circumstances is renting from Zippy cheaper
than renting from A+?
Suppose Sam rents a car from A+ and drives it 225 miles.
What is his rental cost?
Applications Pg. 30
0 Maggie lives 1,250 meters from school. Ming lives 800
meters from school. Both girls leave for school at the same
time. Maggie walks at an average speed of 70 meters per
minute, while Ming walks at an average speed of 40 meters
per minute. Maggie’s route takes her past Ming’s house.
a.
b.
c.
d.
Write equations that show Maggie and Ming’s distances
from school t minutes after they leave their homes
When, if ever will Maggie catch up with Ming?
How long will Maggie remain behind Ming?
At what times is the distance between the two girls less
than 50 meters?
Substitution Method
1. Get both variables on separate sides
2. Get either x or y completely by itself
3. Substitute into the other equation
4. Solve
5. Substitute again to find the second variable value
Substitution Problems
0Page 56 A. 1-6
Combination Method
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Get X and Y on the Same Side
Make Sum of 2 Equations = Sum of Totals
Solve for X
Plug X Back Into an Equation From Step One
Solve for Y
Combination
Problems
0Page 58 A. 1-3
Solve Using Any Method
Pg. 40
0 Write each equation in y=mx + b form.
1. x – y = 4
2. 2x + y = 9
3. 8x + 4y = -12
4. 12 = 3x -6y
5. x + y =2.5
6. 600 = 5x + 10y
Parallel and Perpendicular
Lines Pg. 46
0 Write an equation of a
line parallel to the given
line.
36. y= 4x + 6
37. -6x + y = 3
38. x + y = 9
39. x + 4y = -20
40. Y = -(3/4)x -2
41. 7x + y = -12
Write an equation of a line
perpendicular to the given
line
42. y = -4x +2
43. y = -(2/3)x -7
44. y = 6x +12
45. -2x + y = -1
46. x – 4y = 20
47. 2x + 3y = 8
Parallel and Perpendicular
Lines Pg. 48
0 Without graphing, decide whether the lines are
parallel, perpendicular, or neither.
3x + 6y =12 and y = 10 + -(1/2)x
b. Y = -x +5 and y = x +5
c. Y = 2 – 5x and y = -5x +2
d. Y = -3 +5x and y = -(x/5) +3
e. 10x +5y = 20 and y = 10x + 20
a.
Parallel and Perpendicular
Lines Pg. 47
0 Suppose you are given the line equation ax + by = c.
a. What is the slope of every line parallel to this line?
b. What is the slope of every line perpendicular to this
line?
Coordinates
0 Tell whether each ordered
pair is a solution of 3x –
5y = 15.
(-2, -4)
b. (0, -3)
c. (-10, 9)
d. (-5, -6)
e. (-10, -9)
f. (-4, -5.4)
a.
Which equation is
equivalent to 3x + 5y = 15?
3x = 5y +15
b. x = -5y +5
c. y = 0.6 x +3
d. y = -0.6x + 3
a.
Problem Solving With Graphs
1. Graph both equations
2. Estimate a Point of Intersection
3. Check Your Table to See if You Were Right
4. Determine the Inequality Conditions
5. Shade the Appropriate Area
6. Label your Graph and Conclude
Problem Solving With Graphs
Investigation 5
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