y = x + 4
y = 2x + 5
Mr. Randolph finds that the supply and demand for gasoline at his station are generally given by the following equations.
x - y = -2
x + y = 10
Use the substitution method to find the equilibrium point where the supply and demand lines intersect.
(4, 6)
The solution to the system:
x = 4y
2x + 3y = 22
What is (8, 2)
Two lines that intersect at a point on the graph will have this solution.
one
y = 3x - 2
y = -x - 2
Harvey has some $1 bills and some $5 bills. In all, he has 6 bills worth $22. Let x be the number of $1 dollar bills and y be the number of $5 bills. Write a system of equations to represent the situation to determine how many bills of each denomination he has.
Harvey has (2) $1 bills and (4) $5 bills.
The solution to the system
y = x - 2
3x - y = 16
What is (7, 5)
Parallel lines will have this......
no solution
y = -3
x = 5
Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of friends purchased 8 tickets for $52.75.
Use a system of equations to determine how many adult tickets and student tickets were purchased.
5 adults tickets and 3 students tickets
The solution to the system
y = 3x
7x + 2y = 39
What is (3, 9)
A system of equations that has many solutions is called this.
infinite amount of solutions
y = (1/3)x - 3
y = 2x - 8
A used book store also started selling used CDs and videos. In the first week, the store sold 40 used CDs and videos, at $4.00 per CD and $6.00 per video. The sales for both CDs and videos totaled $180.00.
Graph the system of equations to determine how many CDs and videos were sold the 1st week.
30 CDs and 10 Videos
The solution to the system
3s - 2t = 4
t = 2s
What is (-4, -8)
A system of equations that has the same slope, but not necessarily the same y-intercept will have this solution.
no solution
y = 3x + 2
y = 3x - 2
Two airplanes are in flight near a local airport. One plane is at an altitude of 1000 meters and is ascending at a rate of 400 meters per minute. The second plane is at an altitude of 5900 meters and is descending at a rate of 300 meters per minute.
Make a graph to determine when the planes will be at the same altitude.
The solution to the system
t + u = 12
t = (1/3)u
What is (3, 9)?
y = -1/2 x + 9
y = -1/2 x + 9
infinite amount of solutions