A set of simultaneous linear algebraic equations is represented in a matrix form as shown below.

$\begin{bmatrix} 0 &0 &0 &4 &13 \\ 2& 5& 5& 2& 10\\ 0&0 &2 &5 &3 \\ 0&0 &0 &4 &5 \\ 2& 3 &2 & 1 & 5 \end{bmatrix}\begin{bmatrix} x_{1}\\ x_{2}\\ x_{3}\\ x_{4}\\ x_{5} \end{bmatrix}= \begin{bmatrix} 46\\ 161\\ 61\\ 30\\ 81 \end{bmatrix}$

The value (rounded off to the nearest integer) of $x_{3}$ is ___________