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 Mrs. Brownstone have?
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
y=-2x+5
y=4x-1
(1,3)
Write an example of a system of equations that would most easily be solved using substitution.
one equation has an isolate variable
-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
y=7
y=-3x-7
(-4.67,7)
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?
Ax+By=C
Standard Form
y=4x
y=4x+9
No Solution
y= 20 - 2x
6x -5y =12
(7,6)
-7x - 3y = -5
5x + 6y = 19
(-1, 4)
Wendy is starting a catering business and 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