\[\left( \mathbf{i} \right)~15x\text{ }\text{ }18y\text{ }+\text{ }1\text{ }=\text{ }0,\text{ }12x\text{ }+\text{ }10y\text{ }\text{ }3\text{ }=\text{ }0\]
and
\[6x\text{ }+\text{ }66y\text{ }\text{ }11\text{ }=\text{ }0\]
Given:
\[15x\text{ }\text{ }18y\text{ }+\text{ }1\text{ }=\text{ }0\text{ }\ldots \ldots \text{ }\left( i \right)\]
\[12x\text{ }+\text{ }10y\text{ }\text{ }3\text{ }=\text{ }0\text{ }\ldots \ldots \text{ }\left( ii \right)\]
and
\[6x\text{ }+\text{ }66y\text{ }\text{ }11\text{ }=\text{ }0\text{ }\ldots \ldots \text{ }\left( iii \right)\]
Now, consider the following determinant:
\[=>\text{ }1320\text{ }\text{ }2052\text{ }+\text{ }732\text{ }=\text{ }0\]
Hence proved, the given lines are concurrent.
\[\left( \mathbf{ii} \right)~3x\text{ }\text{ }5y\text{ }\text{ }11\text{ }=\text{ }0,\text{ }5x\text{ }+\text{ }3y\text{ }\text{ }7\text{ }=\text{ }0\text{ }and\text{ }x\text{ }+\text{ }2y\text{ }=\text{ }0\]
Given:
\[3x~-~5y~-~11\text{ }=\text{ }0~\ldots \ldots ~\left( i \right)\]
\[5x\text{ }+\text{ }3y~-~7\text{ }=\text{ }0~\ldots \ldots ~\left( ii \right)\]
And ,
\[x\text{ }+\text{ }2y\text{ }=\text{ }0~\ldots \ldots ~\left( iii \right)\]
Now,
Hence, the given lines are concurrent.