Solution:

The given equations are:
$23 x-29 y=98 \quad \ldots .$ (i)
$29 x-23 y=110 \ldots \ldots$ (ii)
Adding equation(i) and equation(ii), we obtain:
$\begin{array}{l}
52 x-52 y=208 \\
\Rightarrow x-y=4 \quad \ldots \ldots \text { (iii) }
\end{array}$
Subtracting equation(i) from equation(ii), we obtain:
$6 x+6 y=12$
$\Rightarrow \mathrm{x}+\mathrm{y}=2\dots \dots(iv)$
Now, adding equation (iii) and equation(iv), we obtain:
$\begin{array}{l}
2 x=6 \\
\Rightarrow x=3
\end{array}$
On substituting $\mathrm{x}=3$ in equation(iv), we have:
$\begin{array}{l}
3+y=2 \\
\Rightarrow y=2-3=-1
\end{array}$
As a result, $x=3$ and $y=-1$.