I am starting to learn about the use of mass action law in chemistry. I am doing some exercises to practice. In particular, I am considering the reaction $$2 X \underset{3}{\stackrel{4}{\rightleftharpoons}} Y.$$ By mass action law I have obtained the following system of ODE's $$ \left\{ \begin{array}{ l } \frac{d}{dt}x(t)=-8x^2+6y\\ \frac{d}{dt}y(t)=4x^2-3y, \end{array}\label{SEDO} \right.$$
where I have used this result.
I am wondering if it is usual that the amount $x(t)+y(t)$ is not conservated.