Five hundred gallons of 89 - octane gasoline is obtained by mixing 87 - octane gasoline with 92 - octane gasoline . ( a ) Write a system of equations in which one equation represents the total amount of final mixture required and the other represents the amounts of 87 - and 92 - octane gasoline in the final mixture . Let X and y represent the numbers of gallons of 87 - and 92 - octane gasoline , respectively . ( 6 ) use a graphing utility to graph the two equations in part ( a ) in the same viewing window As the amount of 87 - octane gasoline increases , how does the amount of 92 octane gasoline change ? ( C ) How much of each type of gasoline is required to obtain the 500 gallons of 89 - octane gasoline