River Y: c = 42
River Z: c = 5n + 12
Both rivers have the same cost after 6 hours.
The system of equations provided represents the total cost (c) of renting a canoe on two different rivers, Y and Z, as a function of the number of hours rented (n).
For River Y, the cost is a constant $42, while for River Z, the cost is given by the equation $5n + $12, where n is the number of hours.
To find the point of intersection, where the cost is the same on both rivers, we set the two equations equal to each other:
42=5n+12.
By solving this equation for n, we subtract 12 from both sides and then divide by 5:
30=5n,
n=6.
Therefore, the cost of renting a canoe on both rivers is the same when the canoe is rented for 6 hours.
At this point of intersection, the total cost on River Y is $42, and on River Z, it is $5 * 6 + $12 = $30 + $12 = $42.
The solution of n = 6 confirms that after renting the canoe for 6 hours, the cost becomes equal on both rivers, and this point is the common intersection point on the graph of the two cost functions.