Answer
Since $\det(A)= 0$, then the system has no solutions or has infinite number of solutions.
Work Step by Step
Let $A$ be the coefficient matrix which is given by
$$A=\left[ \begin {array}{ccc} 1&2&6\\ 2&5&15
\\ 3&1&3\end {array} \right]=\left[ \begin {array}{ccc} 1&2&6\\ 0&1&3
\\ 0&-5&-15\end {array} \right]
.$$
One can calculate $\det(A)$ as follows
$$\det(A)=(1)(-15)-(3)(-5)=0.$$
Since $\det(A)= 0$, then the system has no solutions or has infinite number of solutions.