Of course they're multiples of 9, because:
When you start going from 1*9 to 11*9, everytime you add a ten, you subtract one unit, going from 9 to 0 (1*9 -> 10*9) and starting back from 9 (11*9), which means that the relation between subtractions and additions of the tenths and oneths remains same:
0 * 9 = 0 (0+9)
1 * 9 = 9 (9+0)
2 * 9 = 18 (8+1)
3 * 9 = 27 (7+2)
4 * 9 = 36 (6+3)
etc.
So, if you choose 1 for tens, you're between 10 and 19. For 9x there's 18. Between 20 and 29 there's 27. Between 30 and 39 there's 36, and so forth.
The higher the number you choose for tens, the lower the 9x will be in units, and the higher the number that you will have to subtract from the number that consists of two numbers, so if you pick 1 for tens, you will end up subtracting 1, which will make your 10 (1 and 0) a 9. If you choose 2, you'll end up with 18. Whatever number you will add as the unit to those tens, it will be subtracted also, which makes it a useless procedure, so you're stuck with choosing a value for the tens, but cause it gets taken off the final result, you will have to go as many units back from the tens, and because of the effect of units going down one step whenever a tenth raises one, the scales will maintain the balance.