Step 1 :Represent the system of equations as a matrix equation of the form AX = B, where A is the matrix of coefficients, X is the column matrix of variables, and B is the column matrix of constants.
Step 2 :Matrix A is \[\begin{bmatrix} -4 & 4 & 2 \\ 1 & 5 & -1 \\ 5 & 1 & -3 \end{bmatrix}\] and matrix B is \[\begin{bmatrix} 16 \\ 19 \\ 3 \end{bmatrix}\].
Step 3 :Use the inverse matrix method to solve for X. This involves finding the inverse of A, if it exists, and then multiplying both sides of the equation by A inverse.
Step 4 :If the inverse of A does not exist, the system is either inconsistent or dependent.
Step 5 :After calculation, we find that X is \[\begin{bmatrix} -0.5 \\ 4.5625 \\ 0 \end{bmatrix}\].
Step 6 :Thus, the solution to the system of equations is \(\boxed{(-0.5, 4.5625, 0)}\).