It is given that

\[3x\text{ }+\text{ }y\text{ }\text{ }2\text{ }=\text{ }0\text{ }\ldots \text{ }\left( 1 \right)\]

\[px\text{ }+\text{ }2y\text{ }\text{ }3\text{ }=\text{ }0\text{ }\ldots \text{ }..\text{ }\left( 2 \right)\]

\[2x\text{ }\text{ }y\text{ }\text{ }3\text{ }=\text{ }0\text{ }\ldots \text{ }\left( 3 \right)\]

By tackling conditions (1) and (3) we get

\[x\text{ }=\text{ }1\text{ }and\text{ }y\text{ }=\text{ }-\text{ }1\]

Here the three lines cross at one point and the place of convergence of lines (1) and (3) will likewise fulfill line (2)

\[p\text{ }\left( 1 \right)\text{ }+\text{ }2\text{ }\left( -\text{ }1 \right)\text{ }\text{ }3\text{ }=\text{ }0\]

By additional computation

\[p\text{ }\text{ }2\text{ }\text{ }3\text{ }=\text{ }0\]

So we get

\[p\text{ }=\text{ }5\]

Henceforth, the necessary worth of p is 5.