Find the value of p, if the following lines are concurrent
$4\mathrm{x}-3\mathrm{y}=7,2\mathrm{x}+\mathrm{py}+2=0,6\mathrm{x}+5\mathrm{y}-1=0$

Let p(x, y) be the point of concurence
$4\mathrm{x}-3\mathrm{y}-7=0 ...\left(1\right), 2\mathrm{x}+\mathrm{py}+2=0 ...\left(2\right)$
$6\mathrm{x}+5\mathrm{y}-1=0\dots .\left(3\right)$
Solving (1) and (3)
$\begin{array}{llll} \mathrm{x}& \mathrm{y}& 1& \\ -3 & -7 & 4& -3\\ 5& -1& 6& 5\end{array}$
$\begin{array}{r}\frac{\mathrm{x}}{3+35}=\frac{\mathrm{y}}{-42+4}=\frac{1}{20+18}\\ \Rightarrow \mathrm{x}=\frac{38}{38}=1,\mathrm{y}=\frac{-38}{38}=-1\end{array}$
point of concurrence(1, –1)
$$\begin{gathered} \text{From(2)⇒2(1)+p(-1)+2=0} \\ \Rightarrow \text{p=4 } \end{gathered}$$