Word Problems
substitution
graphing
vocabulary
systems of inequalities
100
A farmer feeds his cow 200 pounds of feed each day and has 700 pounds of feed in his barn. Another farmer feeds his cows 350 pounds of feed each day and has 1000 pounds of feed in his barn.
In how many days will the two farmers have the same amount of feed left?
How would your answer change if both farmers got an additional 1000 pounds of feed?
1. 2 days
2. 2 days, it would not change since you are giving both farmers the same (equal) amount of feed
100
y = 2
x + 2y = 6
(2,2)
100
x+y=4
2x-5y=15
(5, -1)
100
what are 3 methods of solving systems of equations?
elimination
graphing
substitution
100
when graphing linear inequalities what does < and > mean
Use a Dotted Line
200
The perimeter of a rectangle is 24 in. and its length is 3 times its width. What are the length and width of the rectangle?
width:3
length: 9
200
y = 3x
2x + y = 10
(2,6)
200
y=-2x+3
8x+4y=12
Infinity many solutions
200
y = 2x + 3
y = 2x - 5
Lines with the same slope have:
A) one solution
B) no solution
C) infinite solutions
200
what does ≤ and ≥ mean when graphing linear inequalities
solid line
300
Kevin wanted to throw a birthday party but did not want to spend a ton of money.The Rental place A charges a fee of $50 plus $25 per hour. The rental place B charges a fee of $10 plus $35 per hour. Using systems of equations, answer the following questions. Show all your work.
A. Write a system of equations the represent the situation above. (Be sure to identify the variables.)
B. When will the plans cost the same amount? Explain how you found your solution.
C. Which plan is cheaper at 2 hours?
a.
h:hours
y:total cost
y=25h+50
y=35h+10
b.4 hours
c. B. $80
300
y = 5x - 1
2y = 3x + 12
(2,9)
300
3x - 2y = 8
x + y = 6
(4,2)
300
When will a system of linear equations have no solution?
The lines are parallel or they have the same slope and different y-intercepts or when you solve the equations and get a false statement with no variables remaining.
300
y ≤ x − 2
y > −3x + 5
Shaded below the first line and to the right of the second line
400
There were 300 people at a dance. Tickets cost $5 for visitors and $3 for students. The total ticket sales were $1100. How many visitors and how many students attended the dance?
200 students
100 vistors
400
3y=9x-15
18x=6y+30
Infinitely many solutions.
6x=6x
400
y = 1/2x + 2
y = 1/4x + 4
(8,6)
400
How many solutions does this system have:
y = -5x + 3
2y + 10x = 6
A) one solution
B) no solution
C) infinite solutions
400
How do you know where to shade when solving systems of inequalities?
Test a point in the inequality. If it's true, shade toward the point. If false, shade away from the point. The solution is where the shaded regions overlap.
500
The equations 5x + 2y = 48 and 3x + 2y = 32 represent the money collected from school concert tickets sales during two class periods. If x represents the cost for each adult ticket and y represents the cost for each student ticket, what is the cost for each adult ticket?
x=8
500
x + y = 10
-y = 5 + x
no solution
500
4x - 5y = 15
8x + 5y = 45
(5,1)
500
How can you tell if a linear system has infinitely many solutions?
The equations are the same, the graphed lines lie on top of one another, or solving the system provides a true statement with no variables.
500
y ≤ x − 2
y > −3x + 5