SOLUTION:
The system of equations written in row form is;
[tex]\begin{bmatrix}{1} & {3} & {2} & {2} \\ {-2} & {-2} & {0} & {-12} \\ {-1} & {-2} & {-1} & {-4} \\ {\placeholder{⬚}} & {\placeholder{⬚}} & {\placeholder{⬚}} & {\placeholder{⬚}}\end{bmatrix}[/tex]The reduced row echelon form is;
[tex]\begin{bmatrix}{1} & {0} & {-1} & {8} \\ {0} & {1} & {1} & {-2} \\ {0} & {0} & {0} & {0} \\ {\placeholder{⬚}} & {\placeholder{⬚}} & {\placeholder{⬚}} & {\placeholder{⬚}}\end{bmatrix}[/tex]This shows that the equation has infinitely many solutions.