Hey there!
These are slope intercept equations, because they have an initial cost and then a cost based on an independent variable, in this case, time spent skating.
Given the information, Ice Dreams equation would be c=1.5h+4 and Skating Paradise would be c=3h+1
Now, we just put them together to make the systems of equations.
c=1.5h+4
c=3h+1
Now, we need to find a point where the two will meet, which will give us our answer. We just need to solve the system.
Let's solve using elimination.We can multiply the top equation by -2 so we can use elimination.
-2c=-3h-8
c=3h+1
We combine the equations..
-c==7
c=7
Now we can plug this into one of the other equations.
7=3h+1
h=2
Now, we have our solution..
(h,c)=(2,7)
Therefore, after two hours, the cost will be the same, and the cost will be seven dollars.
I hope this helps!
