Based from Harminc and Sotak's result, www.fq.math.ca/Scanned/36-3/harminc.pdf

We know that under certain condition, an arithmetic progression can contain an infinitely many palindromes.

My question will be, if I have a system of Arithmetic Progression such as

\begin{equation*} 3t+2\tag{1} \end{equation*} \begin{equation*} 4t+1\tag{2} \end{equation*} can I always find an integer $t$ such that $(1)$ and (2) are both palindromes? I know in my example that the answer is yes. But in general, if I have the system

\begin{equation*} pt+j\tag{1} \end{equation*} \begin{equation*} qt+k\tag{2} \end{equation*}

with $\text{gcd}(p,q)=1$, can I find a $t$ for all $j<p$ and for all $k<q$ such that $(1)$ and $(2)$ are both palindrome? I am curious about this but I do not know how to answer it.

Or are there any reading materials that can help me on answering my query? Kindly help me.

Thanks for your help.