Algebra
Solve for x. 2(x + 4) = 5x - 3
x = 11/3
What is the set of all y-values?
Range
What is the range of the following set? {[0,2], [2,2] [3,2]}
2
What methods are used to solve systems of linear equations?
Substitution, Reduction, Equalization
Solve the system: y = 2x , 3y = 5x - 3
x = -3 , y = -6
Solve for x. ½(x -2) = ⅓(2x+5)
x = -16
n the following function, which is the independent variable? T = 1/2x +10
T
Is the following set a function? {[-3,-3], [-1,-3], [0,3], [2,2], [3,3]}
Yes
What method would be the easiest to use to solve the following system? y = 2x + 4 , y = 5x - 7
Equalization
The sum of two numbers is 108, and their difference is 68. What are the numbers?
86 and 18
4x(2+ 1/x) = 3x - 3
x = -7/5
If you can draw a vertical line through a graphed relation and it touches two points of the relation, is it a function?
No
For what values of ‘a’ is the following relation not a function? {[a, 0], [2, 1], [3,1]}
2 or 3
What method would be the easiest to use to solve the following system? 17 = 2x + 3y , 4 = 4x - 2y
Reduction
A farmer owns sheep and chickens. In total he owns 37 animals in total. If the total number of animal legs is 114, how many sheep are there and how many chickens are there?
17 chickens, 20 sheep
Form an algebraic equation given the following information. A rental car costs $15 to rent and then $0.50 per kilometer driven.
y = 15 + 0.5x
In the generic linear equation y = mx + b, which letter represents the slope of the function?
m
If a line has slope 3 and y-intercept of 2. What is the equation of the line?
y = 3x + 2
Solve the system: 2y = 4x + 6 , 3y = 6x + 9
Infinite solutions
A man bought 6 shirts and 8 hats for $700. A week later, at the same prices, he bought 9 shirts and 6 hats for $660. How much does one shirt cost?
$30
A father is 37 years old and his son is 11. In how many years will the father be double the son’s age?
x = 15
Given the generic linear function y = mx + b, what letter represents the y-intercept, or the value of y when x = 0?
b
Given the two points {[0,1], [1,3]} graph the linear function and find the formula in the form y = mx + b
y = 2x + 1
Solve the system: y - 3x = 2 , y = 3x - 2
No solution
Two trains 400km apart are traveling in opposite directions on the same railway. One is traveling at 70km/hr and the other is traveling at 90km/hr. When do the trains meet? How far does each train travel? [Hint: distance = speed x time]
t = 2.5, x = 175 , 225km