Solve the System of Equations Below by the Gaussian Elimination $3 t + 6 u + v - 8 w = - 31$

Multiple Choice

Solve the system of equations below by the Gaussian elimination method: $3 t + 6 u + v - 8 w = - 31$ $t + 3 u - 2 v + 7 w = - 21$ $- 7 t - 2 u + 9 v + 6 w = 23$

A) $\left( \frac { 333 } { 59 } c + 1 , - \frac { 120 } { 59 } c - 6 , \frac { 193 } { 59 } c + 2 , c \right)$
B) $\left( \frac { 333 } { 59 } c + 1 , \frac { 193 } { 59 } c + 2 , - \frac { 120 } { 59 } c - 6 , c \right)$
C) $\left( \frac { 193 } { 59 } c + 2 , \frac { 333 } { 59 } c - 6 , - \frac { 120 } { 59 } c + 1 , c \right)$
D) $\left( - \frac { 120 } { 59 } c - 6 , \frac { 193 } { 59 } c + 1 , \frac { 333 } { 59 } c + 2 , c \right)$
E) no solution