The inductive step is done in two parts.
i) When x>0 (replace x by x-1 and y by y+1 and you have n+1)
ii) When x=0 (replace y by y-1 and x by x+2 and you have n+1)
prove that any integer n> 2 can be written in the form n = 2x + 3y where x, y> 0 are integers.
If $\displaystyle n$ is even then we can write $\displaystyle n = 2x$. If $\displaystyle n>2$ is odd then $\displaystyle n-3$ is even and then $\displaystyle n-3=2x\implies n = 2x + 3$.