"Words of Wisdom"
This is term used to describe the relationship between two or more functions.
What is a system of equations?
Solve this system of equations by substitution:
* d = 3t
* d = 14 - 4t
(2,6)
Solve this system of equations by elimination:
* y + x = 60
* y - x = 20
(20,40)
Dave is going to Coinstar. He has a bag of 30 coins that are only pennies and nickels. The amount in the bag came out to be $0.90. Write a system of equations to determine the number of pennies, p, and the number of nickels, n, that David had in his bag.
p + n = 30
.01p + .05n = 0.90
Two functions are shown below.
f(x) = x2 + x + 5
g(x) = 2x + 7
Which 2 points do the graphs of the two functions intersect.
(-1,5) and (2,11)
A point that is shared between two or more functions.
What is a solution?
What is the value of x for the system of equations:
* y = 1.5x
* y = 12 - 2.5x
3
Solve for y in this system of equations by elimination:
* 6x + 5y = -20
* -6x - 10y = 25
-1
Old McDonald has chickens and goats on his farm. Together, he has 64 animals. He observed that the animals had a total of 188 legs. Write a system of equations used to describe the number of chickens and goats that Old McDonald had.
c + g = 64
2c + 4g = 188
Cullin needs to save at least $100 for homecoming. He works 2 jobs earning $8/hour at Culvers and $25/hour mowing lawns. He only has time to work 14 hours before homecoming. Write a system of in inequalities to describe this scenario.
8x + 25y ≥ 100
x + y ≤ 14
An algebraic method that replaces the value of a variable with an equivalent expression.
What is substitution?
What is the value of x for the following system of equations:
* y = 2/3x
* y = 2x - 8
6
Solve for y in this system of equations by elimination:
* -4x -2y = -12
* 4x + 8y = -24
-6
Christian had brochures printed for a new business venture. Christian originally ordered 4 boxes of black-and-white brochures and 3 boxes of color brochures, which cost a total of $134. After those ran out, Christian spent $120 on 3 boxes of black-and-white brochures and 3 boxes of color brochures. Which system represents this situation?
4x + 3y = 134
3x + 3y =120
How many solutions are in this system:
* 3x + 5y = 30
* 3x + 5y = 60
No solutions
An algebraic method to solve a system of equations by creating opposite coefficients of a desired variable.
What is elimination?
What is the value of x for when f(x) = g(x):
* f(x) = 10x + 18
* g(x) = 4x - 6
-4?
Solve for x in this system of equations by elimination:
*-2x - 9y = -25
* -4x - 9y = -23
-1
David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?
1.50n + 0.50s = 78.50
n + s = 87
How many solutions are in this system of equations:
* 10x - 40y = 70
*100x - 400y = 700
Infinitely many solutions
A method for solving a system of equations by identifying the point of intersection.
What is graphing?
What is the value of x for the solution of y= -5x + 11 and 2x + y = 5
2
Solve for y in this system of equations by elimination:
* -3x + 7y = -16
* -9x + 5y =16
-4
Caitlin won a bag full of money! She has 49 bills in all. She counts $1,430. There are $20 dollar bills and $50 dollar bills. How many of each bill does Caitlin have?
Write a system where T= # of $20 and F = # of $50.
T + F = 49
20T + 50F = 1430
Jada has two dogs. The larger dog weighs 2.4 pounds more than the smaller dog. The combined weight of the two dogs is 14.4 pounds. What is the weight, in pounds, of the smaller dog?
6