Question 2819
Let the two integers be x and y

Sum of two integers  = 10
=> x+y = 10.......eq(1)

Let x > y
So , three time the larger integer is three less then eight times the smaller integer
=> 3x = 8y -3........eq(2)

From equation(1) 
x = 10-y

substituting the value of x in eq(2)
3(10-y) = 8y -3
=> 30 -3y = 8y -3
=> 33 = 11y
=> y = 3
substituting the value of y in eq(1) to get value of x
=> x = 10-3 =7

So the two integers are 7 and 3