Solve the System, If Possible, by Using Cramer's Rule Solve For

Multiple Choice

Solve the system, if possible, by using Cramer's rule. If Cramer's rule does not apply, solve the system by
using another method.
- $$\begin{array} { l } x _ { 1 } + 5 x _ { 2 } - 3 x _ { 3 } - 5 x _ { 4 } = - 6 \\- 3 x _ { 2 } + x _ { 4 } = 4 \\x _ { 1 } + 5 x _ { 3 } = - 2 \\2 x _ { 3 } - 4 x _ { 4 } = - 8\end{array}$$ Solve for $x _ { 3 } .$

A) $\frac { 44 } { 29 }$
B) $\frac { 36 } { 29 }$
C) $\frac { 82 } { 29 }$
D) $- \frac { 28 } { 29 }$