System of 1 st Degree Equations with 2 Variables
Jan 01, 2016
System of 1st Degree Equations with 2 Variables
Solving a system of equations (2 rules) to find the ordered pair (x,y) that is common to both rules•Example: To rent a car you are given 2
choices.Choice A Choice BCosts 0.30¢ per km. Cost is $30 and
then 0.20¢ per km.
Write the rules for each situationChoice A y = 0.30xChoice B y = 0.20x + 30
Question: How many km will you drive for the cost to be the same?
Create 1 Table of Values for both situations
# of km
0 100 200 300 400 500
Choice A
0 30 60 90 120 150
Choice B
30 50 70 90 110 130
If you drive 300 km, the cost will be the same for choices A and B
Graph this situation
50
10
(300,90) x , y
Point of intersection of the 2 lines is called theSOLUTION SET
# of km
cost
•
The point of intersection must match your table of values !!
What and where is the solution set?
What???? • It is the point where the value of x has the same value of y in both situations.
Where????• It is found in the table of values. Look for the x that has the same y value below it.• It is found on the graph. Look to see where the two lines intersect.
Example #2
You have been given the choice of two options for a babysitting job.
Option #1
You will be paid $4 an hour.
Option #2
You will be paid $5 initially and then $3 an hour.
After how many hours will it not matter which payment option you choose?1- write the rules(system of equations) 2- make table of values3- draw the graph 4- answer the question
Table of Values
Write out the rules for the two options
Option #1 y = 4xOption #2 y = 5 + 3x
Hours worked
0 1 2 3 4 5 6 7
Option 1
0 4 8 12 16 20 24 28
Option 2
5 8 11 14 17 20 23 26
Looking at the table of values, the solution set is found at (5, 20). This means that after working 5 hours, you would make $20 regardless of which option you choose.
Graphing to find solutions set
# hours
1
2
Pay
•Solution set(5,20)
Workbook page 122 Activity #1 4306
then do page 124question #1 a,c,dthey give you the rules…you make the table of values and the graph.
Page 124 #1 a
x 0 1 2
Y= 2x +3 3 5 7
Y= -1x +6 6 5 4
x 0 1 0.5
Y=4x +3
3 7 5
Y=8x+1
1 9 5
Comparison Method
Using the algebraic method is much easier and faster than table of values and graphing.
Y = 0.30xY = 0.20x + 30
We want to know when the y is the same…so we make the equations equal to each other
0.30x = 0.20x + 300.30x – 0.20x = 0.20x + 30 – 0.20x0.10x = 300.10 0.10X = 300
Now that you have the x, how do you find the y ???
To find the “y” substitute the answer you got for x into EITHER of the rules…pick the easier one !
Y= 0.30xY = 0.30 • 300Y= 90
Now you have both answers for the solution set…..(300,90)
Example #2: Your family needs to choose between two vacations.MiamiCosts $25oo for airfareCosts $170 per night
New Orleans$2950 airfare$140 per night
Question #1 : How many nights would you stay for the cost to be the same?Question #2 : What would the cost be?
Write the system of equations to begin: Ym = 2500 + 170x
Yn = 2950 + 140x
2500 + 170x = 2950 + 140x2500 + 170x -140x = 2950 +140x -140x2500 + 30x = 29502500 + 30x – 2500 = 2950 -250030x = 45030 30X = 15
Y = 2500 + 170(15)Y= 2500 + 2550Y = 5050
Answers:Question 1 = 15 daysQuestion 2 = $5050
If you want to go for more than 15 nights…which city would be the less expensive?
Miami for 20 nightsY = 2500 + 170(20)y-= 2500 + 3400Y= 5900
New OrleansY=2950 + 140(20)Y= 2950 + 2800Y=5750
Math 4306
For next Tuesday morning you MUST have the following finished:
Page 124 #1 a,b,c,d (use comparison notes) #2Page 125 #3,4Page 127 #7
Be quiet and begin NOW you have 25 minutes to work on this.‘translate this …” means write the 2 rules !
Workbook 396-92page 124 #1 a,b,c,d find solutions set by comparison #2 all
Page 125 allpage 126 allpage 127 allfinish for tomorrow Thursday Feb 4
Math 396-91
Page 125 allpage 126 allpage 127 allFinish for Tues Feb 9
Workbook 306-05 page 122 Activity #1 Choice of two Options
Page 124 #1 a,b,c,d using comparison method #2 a,b,c,d state the variables write the 2 rules find the answer using comparisonPage 125 #3,4
Workbook page 127 #7Page 129 Activity 3Page 132 #5,6Page 143 # 2,3Page 144 #4,6,7Page 145 #9Page 146 #10,11,12Finish for next wednesday
Math 396-92
When done:You may begin your honest numbers project.
Page 145 #9
Rule A y = 300 zeroRule B y = 10x directRule C y = 5x + 100 partial
x 0 10 20 30
Y = 10x 0 100 200 300
Y= 5x + 100 100 150 200 250