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