Problem:
Solve the following system of three equations: 
$-\frac{19 x}{\sqrt{3}}+12 \sqrt{3} y-\frac{4 z}{\sqrt{3}}-\frac{34}{\sqrt{3}}=0$, $\frac{x}{\sqrt{3}}+2 \sqrt{3} y+\frac{16 z}{\sqrt{3}}-\frac{5}{\sqrt{3}}=0$, $\frac{40 x}{\sqrt{3}}-\frac{13 y}{\sqrt{3}}+\frac{41 z}{\sqrt{3}}+5 \sqrt{3}=0$
Answer:
$x=-\frac{38}{775}$, $y=\frac{1419}{1550}$, $z=-\frac{43}{1550}$
{'source': 'AMPS', 'file': 'amps/mathematica/algebra/system_of_equations/37223.txt'}