Maximum Value of 2x + y

From $x + 9 = z$ and $y + 1 = z$, we get: $x + 9 = y + 1 \implies y = x + 8$ Also $z = x + 9$. Substitute $y$ and $z$ into $x + y < z + 5$: $x + (x + 8) < (x + 9) + 5$ $2x + 8 < x + 14 \implies x < 6$ Since $x$ is a non-negative integer, the maximum value of $x$ is $5$. Then $y = 5 + 8 = 13$. Maximum possible value of $2x + y = 2(5) + 13 = 23$.