Question 561849
There is no way that I know to do this algebraically

However we can take 1000 and subtract multiples of 47 until we find a number that is divisible by 19. The easiest way to do this is to use excel. 
=cell above - 47
1000    = cell to the left divided by 19
953	50.15789474
906	47.68421053
859	45.21052632
812	42.73684211
765	40.26315789
718	37.78947368
671	35.31578947
624	32.84210526
577	30.36842105
530	27.89473684
483	25.42105263
436	22.94736842
389	20.47368421
342	18
295	15.52631579
248	13.05263158
201	10.57894737
154	8.105263158
107	5.631578947
60	3.157894737
13	0.684210526


Therefore 342 and 1000-342 is my other number
so 342 and 658