Find the equation of the straight line parallel to the line 3x + 4y = 7 and passing through the point of intersection of the lines x – 2y – 3 = 0 and x + 3y – 6 = 0.

Given lines
$\begin{array}{l}\mathrm{x}+3\mathrm{y}-6=0 .....\left(1\right)\\ \mathrm{x}-2\mathrm{y}-3=0 ....\left(2\right)\end{array}$
Solve (1) & (2)
Point of intersection is $(\mathrm{x},\mathrm{y})=\left(\frac{21}{5},\frac{3}{5}\right)$
$\text{ And given st.line }3\mathrm{x}+4\mathrm{y}=7$
$3\mathrm{x}+4\mathrm{y}-7=0$    ...(3)
Let the eq. of the straight line parallel to (3) and
$\text{ Passing through }\left(\frac{21}{5},\frac{3}{5}\right)\text{ be }$
$$\begin{gathered} \begin{array}{l}3\mathrm{x}+4\mathrm{y}+\mathrm{k}=0\\ \Rightarrow 3\left(\frac{21}{5}\right)+4\left(\frac{3}{5}\right)+\mathrm{k}=0\Rightarrow \mathrm{k}=-15\end{array} \\ \therefore \text{ the eq'n of st.line is }3\mathrm{x}+4\mathrm{y}-15=0 \end{gathered}$$