Evaluate: {2⁢x+3⁢y+5⁢z = 31,2⁢x+4⁢y+7⁢z = 39,3⁢x+2⁢y+z = 22}

Expression: $\left\{2⁢x + 3⁢y + 5⁢z = 31,2⁢x + 4⁢y + 7⁢z = 39,3⁢x + 2⁢y + z = 22\right\}$

$\begin{matrix} x = 5\text{, }y = 2\text{, }z = 3 \\ \end{matrix}$