Solve the simultaneous equations giving your answer in base two
11x+11y=1001
10x-y=11
11x+11y=1001 --- in base 10 ---> 3x +3y = 81 or: x + y = 27
10x - y = 11 ------> 2x - y = 3
add these last two
3x = 30
x = 10 ----in base2: ---> 8+2 = 1*2^3 + 0*2^2 + 1*2^1 + 0 = 1010 (base2)
y = 17 ----in base 2: ---> 16 + 1 --------> 1*2^4 + 0*2^3 + 0*2^2 + 0*2^1 + 1 = 10001 (base2)
11 = 1*2^0 + 1*2^1 = 1+2 = 3
1001 = 1*1 +0*2 +0*4 + 1*8 =9
10 = 0*1 + 2 = 2
3 x + 3 y = 9
or
x + y = 3
2x-y = 3
----------- add
3 x = 6
x = 2 = 10 in base 2
y = 1 in any old base