A computer online service charges one hourly rate for regular use but a higher hourly rate for designated "premium" areas. One customer was charged $38 after spending 2 h in premium areas and 9 regular hours. Another customer spent 3 h in premium areas and 6 regular hours and was charged $34.50. What is the service charge per hour for regular and premium services?

according to the question, One customer was charged $38 after spending 2 h in premium areas and 9 regular hours

Another customer was charged $34.50 after spent 3 h in premium areas and 6 regular hours.

let, the premium services charge per hour=x

let the regular services charge per hour=y

then equation for first customer service charge who spending 2 h in premium areas and 9 regular hours:- 2x+9y=38

now, equation for second customer service charge who spent 3 h in premium areas and 6 regular hours :- 3x+6y=34.50

now use substitution method to solve these equations, To solve a linear equation using substitution method the, first, isolate the value of one variable from any of the equations. Then, substitute the value of the isolated variable in the second equation and solve it. 

from equation first:-  2x+9y=38

x=38/2-9/2 y

x=19-9/2 y (equation 3)

put this value of x in equation 2:- 3x+6y=34.50

3(19-9/2 y)+6y=34.50

57-27/2 y +6y=34.50

6y-27/2 y=34.50-57

-15/2y= -22.5

7.5 y = -22.5

y=22.5/7.5

y=3 ( charges of regular service)

put this value in equation 3:- x=19-9/2 y 

x=19-9/2 *3

x=19-27/2

x=11 / 2

x=5.5 (charges for premium service)