Solve the System Using Gauss-Jordan Elimination $$\left\{ \begin{aligned}x + y + 2 z + t & = 62 \\x + 2 y + z + t & = 62 \\2 x + y + z + t & = 49 \\x + y + z + 2 t & = 62\end{aligned} \right.$$

Multiple Choice

Solve the system using Gauss-Jordan elimination. $$\left\{ \begin{aligned}x + y + 2 z + t & = 62 \\x + 2 y + z + t & = 62 \\2 x + y + z + t & = 49 \\x + y + z + 2 t & = 62\end{aligned} \right.$$

A) $( 2 , - 15,15 , - 15 )$
B) $( - 2,15,15,15 )$
C) $( 2 , - 15,15,15 )$
D) $( 2,15,15,15 )$
E) $( 2,15 , - 15,15 )$