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