Substitute a re-arrangement of the second equation into the first.
2x-y=0 x+y=9
The 2nd Eq (rearranged): y=9-x
Inserted into the first
2x-(9-x)=0
Solved for x
2x-9+x=0
3x=9
x=3 then insert this value of x into one of the original equations, finding y=6