Answer
$(-9, 2, 0)$
Work Step by Step
Step 1. Establish the augmented matrix of the system and use the Gauss Eliminations method:
$\begin{vmatrix} 1 & 2 & -3 & -5 \\ -2 & -4 & -6 & 10\\3 & 7 & -2 & -13 \end{vmatrix} \begin{array}(. \\2R_1+R_2\to R_2\\R3-3R_1\to R_3\\ \end{array}$
Step 2. Perform operations as listed to the right side of the matrix:
$\begin{vmatrix} 1 & 2 & -3 & -5 \\ 0 & 0 & -9 & 0\\0 & 1 & 4 & 2 \end{vmatrix} \begin{array}(. \\.\\.\\ \end{array}$
Step 3. The second row gives $z=0$, and the third row gives $y=2$, first row gives $x+2\times2=-5$ or $x=-9$.
Thus the solution is $(-9, 2, 0)$
