Solution:

The given eq. are:
$\frac{x+y-8}{2}=\frac{x+2 y-14}{3}=\frac{3 x+y-12}{11}$
i.e., $\frac{x+y-8}{2}=\frac{3 x+y-12}{11}$
On cross multiplication, we obtain:
$\begin{array}{l}
11 x+11 y-88=6 x+2 y-24 \\
\Rightarrow 11 x-6 x+11 y-2 y=-24+88 \\
\Rightarrow 5 x+9 y=64\dots \dots(i)
\end{array}$

$\begin{array}{l}
\text { and } \frac{x+2 y-14}{3}=\frac{3 x+y-12}{11} \\
\Rightarrow 11 x+22 y-154=9 x+3 y-36 \\
\Rightarrow 11 x-9 x+22 y-3 y=-36+154 \\
\Rightarrow 2 x+19 y=118 \quad \ldots \ldots \text { (ii) }
\end{array}$
Upon multiplying equation(i) by 19 and equation(ii) by 9 , we obtain:
$95 \mathrm{x}+171 \mathrm{y}=1216\dots \dots(iii)$
$18 \mathrm{x}+171 \mathrm{y}=1062\dots \dots(iv)$

On subtracting equation(iv) from equation(iii), we obtain:
$\begin{array}{l}
77 \mathrm{x}=154 \\
\Rightarrow \mathrm{x}=2
\end{array}$
On substituting $\mathrm{x}=2$ in equation(i), we obtain:
$\begin{array}{l}
10+9 y=64 \\
\Rightarrow 9 y=(64-10)=54 \\
\Rightarrow y=6
\end{array}$
As a result, the solution is $\mathrm{x}=2$ and $\mathrm{y}=6$