Solve the simultaneous equation and written in base two

Question

11x+10y=1000
10x-y=10

Answer 1

change to base 10
11x + 10y = 1000 ----> 3x + 2y = 8
10x - y = 10 -----------> 2x - y = 2

double the second: 4x - 2y = 4
add to the first:
7x = 12/7
x = 12/7
y = 10/7 , in base 10

back to base 2
10(base10) = 1010
12(base10) = 1100
7(base10) = 111

so x = 1100/111
y = 1010/111

or, you could set up an addition and a multiplication table in base 2 and do the
arithmetic in base 2 directly

11x + 10y = 1000 , now multiply the 2nd by 10
100x - 10y = 100
add them
111x = 1100
x = 1100/111 , etc, same answer as above

Answer 2

since y = 10x-10, use that to get
11x+10(10x-10) = 1000
11x + 100x - 100 = 1000
111x = 1100
x = 1100/111
y = 10x-10 = 11000/111 - 1110/111 = 1010/111