Question

11x - 10y=10001
10x - y=10

Answer 1

from the 2nd:
y = 10x - 10

sub into the 1st:
10x - 10(10x - 1) = 10001
10x - 100x + 10 = 10001
-90x = 9991
x = 9991/-90 = - 9991/90

with all those 0's and 1's is this supposed to be in base 2 ?????
in that case, you might want to change it back into base 10
11x - 10y=10001 in base 2 becomes : 3x - 2y = 17
10x - y=10 in base 2 becomes : 2x - y = 2 or y = 2x-2
use substitution,
3x - 2(2x-2) = 17
3x - 4x + 4 = 17
-x = 13
x = -13
then y = -28

now convert back to base 2
13 = 8 + 4 + 0 + 1 = 1101₂ , so x = - 1101
28 = 16 + 8 + 4 + 0 + 0 = 11100₂ , and y = -11100