Graphically (using Geogebra)
Algebraically using Substitution
Algebraically using elimination
Word Problems
General Knowledge
100
Find the solution to the System:
y = -1
x = 4
(4,-1)
100
Find the value of each item: (You DO NOT have to solve the last line)
c = crown
d = diamond
h = heart
c = 7
d = 3
h = 2
100
A local market has just released an advertisement. In this ad, it shows the following information. (IGNORE THE LAST LINE):
- 3 pumpkins cost $15
- 6 packages of blueberries and 1 pumpkin costs $65
- 3 packages of blueberries cost $22 more than 2 fennel bulbs
Find the price of one unit of each fruit
p = pumpkin
b = package of blueberries
f = fennel bulb
p = 5
b = 10
f = 4
100
The sum of two numbers is 23 and their difference is 5. Create a system of equations to represent this.
Let x = the first number
Let y = the second number
x + y = 23
x - y = 5
100
How many different variables are in the following system of equations?
3k = 9
k + 2o = 9
o + 2b = 9
There are 3 different variables:
k
o
b
200
Find the solution to the System:
y = -2x + 2
y = -2x - 2
No solution
200
Find the value of each item: (You DO NOT have to solve the last line)
r = red flower
p = pink flower
y = yellow flower
r = 5
p = 3
y = 9
200
x + y = 18
x - y = 12
x = 15
y = 3
200
Aidan and his sister Ella are having a race. Aidan runs at a rate of 10 feet per second. Ella runs at a rate of 6 feet per second. Since Ella is younger, Aidan is letting her begin 30 feet ahead of the starting line.
Let y represent the distance from the starting line and x represent the time elapsed, in seconds.
Write a system of equations, with one to represent the distance Aidan travelled and the other to represent the distance Ella traveled.
E: y = 6x + 30
A: y = 10x
200
DOUBLE POINTS OPPORTUNITY:
Name the following properties:
1) 3 - x = x - 3
2) 4(2y + 5) = 8y + 20
Must get both right for double pointS
1) commutative property
2) distributive property
300
Find the solution to the System:
y = 6x - 6
y = 2(3x - 3)
Infinitely Many Solutions
300
Solve for x and y:
x = 7
y = 3x - 5
x = 7
y = 16
300
Solve the system using the elimination method:
2x - y = 3
3x + y = 12
(3,3)
x = 3
y = 3
300
A small sandwich shop sells burritos and subs. On one day, they sell 5 burritos and 2 subs for $48. On the next day, they sell 3 burritos and 2 subs for $32. Set up a system of equations used to represent the burrito and subs for both days.
5x + 2y = 48
3x + 2y = 32
300
What is the minimum amount of equations needed to make up a system of equations?
2 or more
400
DOUBLE POINTS OPPORTUNITY!
When Graphing a system of equations, how do we know if the system has no solutions? How do we know if the system has infinitely many solutions? Must get both for double points
No solution - parallel lines that do not intersect
infinitely many solution - lines overlap one another (shows one line on the graph)
400
Solve for x and y
y = 3x - 5
y = 4x
x = -5
y = -20
400
An ice cream shop sells small and large sundaes. One day, 30 small sundaes and 50 large sundaes were sold for $420. Another day, 15 small sundaes and 35 large sundaes were sold for $270. Sales tax is included in all prices.
If x is the cost of a small sundae and y is the cost of a large sundae, write a system of equations to represent this situation.
30s + 50L = $420
15s + 35L = $270
400
Your teacher is giving you a test worth 100 points containing 40 questions. On the test, there are multiple choice questions, (m) worth two points each and open ended questions (o) worth 4 points each. Create a system of equations. (Hint: Create two equations: one to represent the number of points on the test and another to represent the number of questions on the test.)
2m + 4o = 100
m + o = 40
400
When solving a system of equations graphically, describe what we look for on the graph.
Where the lines intersect
500
Solve the following system
y - 2x = 8
4x + 3y = 24
x = 0
y = 8
(0,8)
500
Solve for x and y:
x - y =4
3x + 2y = 32
x = 8
y = 4
500
At an amusement park, the cost for an adult admission is a, and for a child the cost is c. For a group of six that included two children, the cost was $325.94. For a group of five that included three children, the cost was $256.95. All ticket prices include tax.
Write a system of equations, in terms of a and c, that models this situation.
2c + 4a = 325.94
3c + 2a = 256.95
500
The sum of the two numbers is 55 and their difference is 41. Find the value of both numbers
48 and 7
500
DOUBLE POINTS OPPORTUNITY
What are three methods in which we can solve a system of equations? (Name at least 2 of the 3) Will receive double points if all 3 are named correctly
1. Graphically with Geogebra
2. Algebraically with substitution
3. Algebraically with elimination