If
then we should have
Differentiating with respect to 
gives
So 
is indeed conservative, and
Let x and y represent the hourly rates of the first and second mechanics, respectively.
.. x + y = 205 . . . . . . . the sum of the two rates was $205 per hour
.. 5x +15y = 1925 . . . . they charged a total of $1925
Divide the second equation by 5, then subtract the first equation.
.. x +3y = 385
.. (x +3y) -(x +y) = (385) -(205)
.. 2y = 180
.. y = 90
.. x = 205 -y = 115
The first mechanic charged $115 per hour; the second charged $90 per hour.
Question 1 has infinitely many solutions and question 2 has only one solution.
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