(d) For the system of given homogeneous equations
$\Delta = \left| {\,\begin{array}{*{20}{c}}1&{\,\,1}&{ - 1}\\3&{ - 1}&{ - 1}\\1&{ - 3}&{\,\,1}\end{array}\,} \right| = 1( - 1 - 3) - 1(3 + 1) - 1( - 9 + 1)$
$ = - 4 - 4 + 8 = 0$. There are infinite number of solutions.