Substitution in two coupled Ito SDEs

Question

Suppose we have the set of simple coupled stochastic differential equations (SDEs) in Ito form \begin{align*} \mathrm{d}X & =\left\{ c_{x}X+c_{xz}Z\right\} \text{d}t+\left\{ c_{z}Z\right\} \mathrm{d}W\left(t\right)\,,\\ \mathrm{d}Z & =\left\{ -c_{xz}X\right\} \mathrm{d}t+\left\{ c_{z}\left(1-Z^{2}\right)\right\} \mathrm{d}W\left(t\right) \,, \end{align*} where $X$ and $Z$ are real variables of the time, $t$. Could we eliminate $X$ from the description and write a single equation for the Z dynamics? I suppose it would have to be a second-order-in-time equation. I am not sure how to proceed, any pointers in the right direction, such as a chapter of textbook or your approach to this would be appreciated.