[tex] \bf \begin{cases}
y=3x+2\\
-3x+y=2\\
3x-y=-2\\
------\\
6x-2y=10
\end{cases}\implies
\begin{cases}
3x-y=-2\\
6x-2y=10
\end{cases}\implies
\begin{bmatrix}
3&-1&|&-2\\
6&-2&|&10
\end{bmatrix}\\\\
------------------------------- [/tex]
[tex] \bf \stackrel{\textit{system's determinant}}{
\begin{bmatrix}
3&-1\\6&-2
\end{bmatrix}\implies (3\cdot -2)-(6\cdot -1)}\implies -6-(-6)\implies -6+6\implies 0
\\\\\\
\stackrel{\textit{systerm determinant of 0 means}}{\textit{the system has \underline{no solutions } or \underline{infinitely many solutions}}} [/tex]
