Given
(i)
$$
\begin{aligned}
& \mathrm{C}(\text { graphite })+\mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g}) \text {; } \\
& \Delta r \mathrm{H}^{\circ}=x \mathrm{~kJ} \mathrm{~mol}^{-1}
\end{aligned}
$$
(ii)
$$
\begin{aligned}
& \mathrm{C}(\text { graphite })+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g}) ; \\
& \Delta \mathrm{rH}^{\ominus}=y \mathrm{~kJ} \mathrm{~mol}^{-1}
\end{aligned}
$$
(iii)
$$
\begin{aligned}
& \mathrm{CO}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g}) ; \\
& \Delta \mathrm{rH}^{\ominus}=\mathrm{z} \mathrm{~kJ} \mathrm{~mol}^{-1}
\end{aligned}
$$
Based on the above thermochemical equations, find out which one of the following algebraic relationships is correct?
