How to I solve system of simultaneous equations (3x3)?

The quickest way would be to find determinants of the matrix; this way we can verify whether the matrix has unique (then we can directly calculate it) solution, infinite number of solutions or no solution. If it has infinite number of solutions, then we need equate one of the variables to some term "t" and express other variables in terms of "t". Alternatively, we can use the method involving substitution and elimination, which can nonetheless take more time, as comapred to determinants method, if the solution is unique.