Linear Equations
If (3 / 11)*x = (2/13), what is the value of x?
What is: 22/39?
3x - y = 11
x + 5y= 9
What is the solution (x, y) of the equations above?
What is: (4, 1)?
Mr. Jensen made 135 copies of an exam for his three classes. If he made 25 fewer copies for his first class than he did for his second and third classes combined, how many copies did he make for his first class?
What is: 55?
This value in a linear equation represents both:
1) the starting value of the dependent variable
2) is the point where the line intersects the vertical axis.
What is: the y-intercept?
If 13 - 3x is 5x less than 9, what is the value of 2x?
x + 3y = 43
2x - 2y = -18
According to the equations above, what is the value of x?
What is: 4?
A post office sells first-class stamps in sheets of 10 or 20 stamps.
An office manager purchased 70 sheets of stamps with a total of 1,080 stamps.
How many of the sheets purchased by the office manager had 20 stamps?
What is 38?
This is the term for the point that satisfies both equations in a system of equations when graphed — it represents the solution to the system.
What is: the point of intersection
(2x - 3 )/4 + (5x + 1)/6 = (7x -2)/3
What is: x=1/12?
4x - y = 6
ax - by = 18
In the system of equations above, a and b are constants.
If the system of equations has infinitely many solutions, what is the value of a/b?
What is: 4?
Two trains leave from the same station, traveling in opposite directions. Train A travels at a constant speed. Train B leaves at the same time and travels 15 miles per hour faster than Train A. After 4 hours, the two trains are 460 miles apart. What is the speed of each train?
Train A: 50 mph
Train B: 65 mph
This quantity describes the rate of change between two variables and is constant in any linear relationship.
What is: the slope?
[3(x-2)]/5 + [2(4x+1)]/3 = (7x+6)/2
What is x= -106/7
25x - 10y = 20
5x + cy = 15
In the system of equations above, c is a constant. If the system has no solution, what is the value of c?
What is: c=-2?
Two cyclists, Alex and Jordan, are training on a 60-mile course. Alex starts first and rides at a constant speed. One hour later, Jordan starts the same course and rides at a speed that is 4 miles per hour faster than Alex's. Jordan catches up with Alex after riding for 3 hours. What are the speeds per hour of Alex and Jordan?
Alex's speed: 12 mph
Jordan's speed: 16 mph
This form of a linear equation is most efficient when you are given a single point on a line and the rate of change (the slope), and it emphasizes how the dependent variable changes relative to the independent one.
What is: point-slope form?