Question

11x+11y=1001

10x_y=11

Answer 1

assuming all are base 2, divide the 1st equation by 11, and you have

x+y = 11
10x-y = 11
now add to get
11x = 110
x = 10
y = 1
check:
110+11 = 1001 ✅
100-1 = 11 ✅