Show that the lines $2\mathrm{x}+\mathrm{y}-3=0, 3\mathrm{x}+2\mathrm{y}-2=0\text{ and }2\mathrm{x}-3\mathrm{y}-23=0$ are concurrent and find the point of concurrency

Given lines
(1) & (2)
$\begin{array}{cccc} & \mathrm{x}& \mathrm{y}& 1\\ 1& -3& 2& 1\\ 2& -2& 3& 2\end{array}$

Now point of intersection of (1) and (2) is
$\frac{\mathrm{x}}{-2+6}=\frac{\mathrm{y}}{-9+4}=\frac{1}{4-3}$
$$\begin{gathered} \frac{\mathrm{x}}{4}=\frac{\mathrm{y}}{-5}=\frac{1}{1} \\ \mathrm{P}=(\mathrm{x},\mathrm{y})=(4,5) \end{gathered}$$
$\mathrm{Sub} \mathrm{P}\text{ in the line }2\mathrm{x}-3\mathrm{y}-23=0$
$\begin{array}{l}2\left(4\right)-3\left(5\right)-23=0\\ 8+15-23=0\Rightarrow 0=0\end{array}$
$\therefore \text{ Given lines are concurrent }$