Question

What is incorrect in this? And how do I correct it?

Answer 1

$\bf \begin{cases} y=3x+2\\ -3x+y=2\\ 3x-y=-2\\ ------\\ 6x-2y=10 \end{cases}\implies \begin{cases} 3x-y=-2\\ 6x-2y=10 \end{cases}\implies \begin{bmatrix} 3&-1&|&-2\\ 6&-2&|&10 \end{bmatrix}\\\\ -------------------------------$

$\bf \stackrel{\textit{system's determinant}}{ \begin{bmatrix} 3&-1\\6&-2 \end{bmatrix}\implies (3\cdot -2)-(6\cdot -1)}\implies -6-(-6)\implies -6+6\implies 0 \\\\\\ \stackrel{\textit{systerm determinant of 0 means}}{\textit{the system has \underline{no solutions } or \underline{infinitely many solutions}}}$