1. HAND IN HOMEWORK

2. POP QUIZ
Take out a piece of loose-leaf

3. System of 1st Degree Equations with 2 Variables

4. 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 B
Costs 0.30¢ per km Cost is $30 and then 0.20¢ per km.
Write the rules for each situation
Choice A y = 0.30x
Choice B y = 0.20x + 30

5. Question: How many km will you drive for the cost to be the same?
Create 1 Table of Values for both situations
# of km
100
200
300
400
500
Choice A 30 60 90
120
150
Choice B 50 70
110
130
If you drive 300 km, the cost will be the same for choices A and B

6. • Graph this situation cost50 10
cost
Point of intersection of the 2 lines is called the
SOLUTION SET •
(300,90)
x , y
The point of intersection must match your table of values !!
# of km

7. What and where is the solution set?
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.

8. 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) make table of values
3- draw the graph 4- answer the question

9. Step 1 - Write out the rules for the two options
Option #1 y = 4x
Option #2 y = 5 + 3x
Step 2 – Table of Values
Hours worked 1 2 3 4 5 6 7
Option 1 8 12 16 20 24 28
Option 2 11 14 17 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.

10. Graphing to find solutions set2
Pay •
Solution set
(5,20) 1
# hours

11. Comparison Method
Using this algebraic method is much easier and faster than table of values and graphing.
We want to know when the y is the same…so we make the equations equal to each other
Y = 0.30x
Y = 0.20x + 30
0.30x = 0.20x + 30
0.30x – 0.20x = 0.20x + 30 – 0.20x
0.10x = 30
X = 300

12. 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 !
Now you have both answers for the solution set…..
(300,90)
Y= 0.30x
Y = 0.30 • 300
Y= 90

13. Example #2: Your family needs to choose between two vacations.
Miami
Costs $25oo for airfare
Costs $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?