ANSWER
The price of the gallons of regular is $2.52
The price of the gallons of premium is $1.52
Explanation
Given information
The total cost of 6 gallons of regular and the7 gallons of premium = $34.09
The gallons of premium gasoline cost $0.19 more per gallon than gallons of regular.
Let x represents the gallons of premium gasoline
Let y represents the gallons of regular
The next step is to set up the system of linear equations.
For the first information, we have 7 gallons of premium and 6 gallons of regular gasoline
Recall, gallons of premium is $0.19 more per gallon in regular
Mathematically
The next step is to solve the equation simultaneously using the substitution method'
Substitute the value of x in equation 2 into equation 1
Hence, the price of the gallons of regular is $2.52
The next step is to find the value of x
Hence, the price of the gallons of premium is $1.52