Graphing
1a) How do you know a system of equations has infinite solutions by graphing?
The lines are on top of each other!
y=-2
4x - 3y = 18
(3, -2)
Identify the opposites in this system of equations.
4x - 3y =27
-2x+ 3y = -21
-3y and 3y will cancel out because the coefficents are opposites
You went downtown with your family and decided to rent segways to roam around town. It costs $25 to rent a segway and the $ 0.10 per minute you are riding it.
a) What is the independent and dependent variable?
b) What is the total cost if you ride 0 minutes?
a) Independent - number of minutes, Dependent- total cost in dollars
b) $25
How many siblings does Ms. Everett have?
2
4) Solve the systems by graphing. You must have a graph drawn with 4 distinct points.
f(x) = 3x - 4
x=3
(3,5)
y = 6x - 21
y= 3(2x - 7)
Infinite Solutions
Write an example of a system of equations that would most easily be solved using elimination.
Variables are lined up so that we can easily add like terms.
You sell teddy bears and dolls. A total of 33 toys were sold earning $400 in sales for your toy store. Each teddy bear cost $8 and each doll cost $12.
Write a system of equations that could be used to determine the number of toys the business sold (DO NOT SOLVE).
x + y = 33
8x + 12 y = 400
The equation t = 6m +13 models the total cost, t, in dollars to drive m miles in an uber. The total cost consists of a flat flee plus a charge per mile driven. When the equation is graphed, what does the y-intercept of the represent in terms of the model?
a) a flat fee of 13 dollars
b) a charge per mile of 6 dollars
c) a charge for mile of 13 dollars
d) total daily charges of 29 dollars
e) none of the above
A
Number 5 in the study guide. Must have a graph with 4 distinct points on white board to support answer.
(-3, -1)
Write an example of a system of equations that would most easily be solved using substitution.
one equation has an isolate variable
14)
-2x - 5y = -1
2x + 10y = 10
(-4, 1.8)
What is the rate of change in this problem?
You went downtown with your family and decided to rent segways to roam around town. It costs $25 to rent a segway and the $ 0.10 per minute you are riding it.
$0.10 per minute
What formula should we use when we have an independent and dependent relationship?
y=mx+b
slope-intercept form
Number 6 in study guide. (Front page)
No solutions
When solving a system of equations my final answer should always be written as .....
an ordered pair
12x - 10y = 30
10y -12x = 30
No Solutions
You love animals so you applied for a job at the Zoo. You would make $10 an hour with a $50 signing at the start.
Create a linear equation to model the situation described.
y = 10x +50
What formula should we use when there is no clear relationship between the variables?
Standard Form
Number 8 in study guide (second page)
Infinite Solutions
y= 20 - 2x
6x -5y =12
(7,6)
-7x - 3y = -5
5x + 6y = 19
(-1, 4)
Wendy is starting a catering business and is attempting to figure out who she should be using to transport the
food to different locations. She has found two trucking companies that are willing to make sure her food arrives intact. Peter’s Pick-Up charges $0.40 per mile and charges a flat fee of $68. Helen’s Haulers charges $0.65 per mile and charges a flat fee of $23.
a) For what distance would the cost of transportation be the same for both companies? What is that cost?
x = 180 miles
y = $140
Graph two lines that are not parallel, but also do not intersect on the visible coordinate plane.
Draw an example on whiteboard