Overview
Solving Systems: Graphing
Solving Systems: Substitution
Solving systems:
Elimination
Elimination
Word Problems are a Problem
100
What shape will every linear equation create when graphed ?
What is a straight line?
100
When should you use the graphing method to solve a system of linear equations?
when questions are written in slope-intercept form ...
aka when the equations are easy to graph.
100
When should you use the substitution method to solve a system of linear equations?
when you already know the value of one variable ( ex: y=6)
100
-7x - 6y = 14
7x -3y = -14
x = -2
y =0
100
A city parking garage charges a flat rate of $3.00 for parking 2 hours or less, and $0.50 per hour for each additional hour. Write a linear model that gives the total charge in terms of additional hours parked.
What is y=.5x+3?
200
At least how many equations will be in a system of linear equations?
What is at least 2 equations?
200
What is the solution to the system of linear equations?
(0,2)
200
What is the solution (x,y) to the system of linear equations?
5x+2=y
x=2
(2,12)
200
-4x - y = 18
4x - 6y = 24
x = -3
y = -6
200
Six 2 foot tall pine trees were planted during the school's observation of Earth Awareness Week in 1990. The trees have grown at an average rate of 34 foot per year. What does the x and y variables represent in our equation?
What is time since tree was planted (x) and how tall tree is (y)?
300
Two ways of solving a system of equations is
What is elimination or substitution?
300
What is the solution to the system of linear equations?
(-1,4)
300
What is the solution to the system?
y=7x-10
y=-3
(1,-3)
300
-12x + 6y = -6
-6x + 3y = -6
no solution
300
Joe and Steve are saving money. Joe starts with $105 and saves $5 per week. Steve starts with $5 and saves $15 per week. After how many weeks do they have the same amount of money?
y=5x+105
y=15x+5
What is 10 weeks ($155)?
400
When two lines intersect that is called a ___________ and is represented by _____________ ___________.
What is a solution and ordered pairs?
400
What is the solution to the system of linear equations?
(2,9)
400
What is the solution to the system?
2x+5y=19
y=3x-3
(2, 3)
400
-3x + 6y = -3
x - 8y = -17
x = 7
y = 3
400
Mike and Sarah collect rocks. Together they collected 50 rocks. Mike collected 10 more rocks than Sarah. How many rocks did each of them collect?
M + S = 50
M = S + 10
What is Mike collected 30 rocks, Sarah collected 20 rocks?
500
True of False
You must eliminate or substitute the y-value first.
What is false?
500
What is the solution to the system of linear equations?
No solutions
500
What is the solution to the system?
5x-6y=-3
y=3x+7
(-3,-2)
500
-36x - 9y = 0
8x + 2y = 0
infinity many solutions, any number combination will work.
500
Molly is throwing a beach party. She still needs to buy beach towels and beach balls. Towels are $3 each and beachballs are $4 each. She bought 10 items in total and it cost $34. How many beach balls did she get?
t+b=10
3t+4b=34
What is 4 beachballs (6 towels)?