Answer:
Solution of the given equations is (-5,2)
Step-by-step explanation:
We have been given the following system of equations:
y = (2/5)x + 4
y = 2x + 12
The solution of the system of equation can be found by finding the point of intersection of both lines on the graph. The graph of both equations is attached below.
As we can see that both the lines intersect each other at one point, and that point is (-5,2). So the solution of the given equations is (-5,2)
The total cost includes the setup cost + per hour cost.
Let, x represents the time and y represents the total cost.
.... (1)
Let Y represent the cost for B's DJ service.
.... (2)
a. Graphing both the equations give the intersection point (solution) as (4,500)
It means for 4 hours, the total cost of both the DJ's is same at $500.
b. Substitution Method.
Plug y = 125x in equation (1)
Hence, the total cost for 4 hours in both the service is $500.
c. Addition method.
Multiply equation (2) by -1
.... Equation (3).
Add euation (1) and equation (3)
Solution: For x = 4, y = 500 ( same as the previous two methods)
For x = 2, equation (1)
For x = 2, equation (2)
Hence, for 2 hours, DJ B would be a better choice since it would charge $250.
For x = 6 hours, equation (1)
For x= 6, equation (2)
For 6 hours, DJ A would be better option since it charges $650 for 6 hours.
