Solve system $$ \begin{aligned} 0 &= 0 \\[1 em] 0 &= 0 \end{aligned} $$

This system has infinitely many solutions.

STEP 1: Find coefficient matrix $ ( D )$, X matrix $ ( D_x ) $ and Y matrix $ ( D_y ) $. In this example we have.$$ D = \left[ \begin{array}{cc} 0 & 0 \\ 0 & 0 \end{array} \right] \quad D_x = \left[ \begin{array}{cc} 0 & 0 \\ 0 & 0 \end{array} \right] \quad D_y = \left[ \begin{array}{cc} 0 & 0 \\ 0 & 0 \end{array} \right] $$

STEP 2: Find determinants $ D $, $ D_x $ and $ D_y $.$$ \begin{aligned} det(D) &= \left| \begin{array}{cc} 0 & 0 \\ 0 & 0 \end{array} \right| = 0 \cdot 0-0\cdot0 = 0 \\ det(D_x) &= \left| \begin{array}{cc} 0 & 0 \\ 0 & 0 \end{array} \right| = 0 \cdot 0-0\cdot0 = 0 \\ det(D_y) &= \left| \begin{array}{cc} 0 & 0 \\ 0 & 0 \end{array} \right| = 0 \cdot 0-0\cdot0 = 0 \end{aligned} $$

STEP 3: Since $ D = 0 $ , $ D_x = 0 $ and $ D_y = 0$, we conclude that system has infinitely many solutions.