Consider the condition of the line having equivalent captures on the tomahawks as

\[x/a\text{ }+\text{ }y/a\text{ }=\text{ }1\]

It tends to be composed as

\[x\text{ }+\text{ }y\text{ }=\text{ }a\text{ }\ldots \text{ }..\text{ }\left( 1 \right)\]

By addressing conditions \[4x\text{ }+\text{ }7y\text{ }\text{ }3\text{ }=\text{ }0\] and \[2x\text{ }\text{ }3y\text{ }+\text{ }1\text{ }=\text{ }0\] we get

\[x\text{ }=\text{ }1/13\] and \[y\text{ }=\text{ }5/13\]

\[\left( 1/13,\text{ }5/13 \right)\] is the mark of crossing point of two given lines

We realize that condition (1) goes through point \[\left( 1/13,\text{ }5/13 \right)\]

\[1/13\text{ }+\text{ }5/13\text{ }=\text{ }a\]

\[a\text{ }=\text{ }6/13\]

So the condition (1) goes through \[\left( 1/13,\text{ }5/13 \right)\]

\[1/13\text{ }+\text{ }5/13\text{ }=\text{ }a\]

We get

\[a\text{ }=\text{ }6/13\]

Here the situation (1) becomes

\[x\text{ }+\text{ }y\text{ }=\text{ }6/13\]

\[13x\text{ }+\text{ }13y\text{ }=\text{ }6\]

Henceforth, the necessary condition of the line is \[13x\text{ }+\text{ }13y\text{ }=\text{ }6.\]