If we first identify our variables, x will be the larger number and y will be the smaller number. We can now identify our equations.
x=1000+2y
x-y=9000
I now have a system of equations, so I can solve for x and y.
1000+2y-y=9000
y=8000
x-8000=9000
x=17000
The larger number is 17000 and the smaller number is 8000.