#### Answer

$x_{1}=1$
$x_{2}=1$
$x_{3}=1$
$x_{5}=1$

#### Work Step by Step

$x_{1}+3x_{4}=4 \rightarrow x_{1}=4-3x_{4}$
$2x_{2}-x_{3}-x_{4}=0$
$3x_{2}-2x_{4}=1$
$2x_{1}-x_{2}+4x_{3}=5$
Substitute $x_{1}$ from the first equation to the fourth
$2(4-3x_{4})-x_{2}+4x_{3}=5$
Simplify and express $x_{2}$ from the equation above.
$x_{2}=3-6x_{4}+4x_{3}$
Substitute $x_{2}$ to the second and the third original equation.
$2(3-6x_{4}+4x_{3})-x_{3}-x_{4}=0$
$3(3-6x_{4}+4x_{3})-2x_{4}=1$
Simplify.
$-13x_{4}+7x_{3}+6=0$
$-20x_{4}+12x_{3}+9=1$
Express $x_{3}$ from the first equation and substitute it to the second.
$x_{3}=\frac{13x_{4}-6}{7}$
$-20x_{4}+12(\frac{13x_{4}-6}{7}) +9=1 \rightarrow $ Simplify.
$x_{4}=1$
Use the value of $x_{4}$ to calculate $x_{3}$, $x_{2}$ and $x_{1}$.
$x_{3}=\frac{13x_{4}-6}{7}=1$
$x_{2}=3-6x_{4}+4x_{3}=1$
$x_{1}=4-3x_{4}=1$