The following simultaneous equations are written in base two

LaTeX: 11x+10y=1000111x+10y=10001

LaTeX: 10x-y=1010x−y=10

Solve the equation, leaving your answer in base two. (6 marks)

why insert the useless LaTeX tags? It's just text.

And poorly copied, at that.

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

multiply the bottom by 10, and you have
11x + 10y = 10001
100x - 10y = 100
now add to eliminate y
111x = 10101
x = 11
Now you can find y
(and yes, I did some thinking in decimal while writing the text)