Problem:
Solve the following system of two equations: 
$9 \sqrt{3} x-\frac{34 y}{\sqrt{3}}-3 \sqrt{3}=0$, $\frac{2 x}{\sqrt{3}}-\frac{y}{\sqrt{3}}-14 \sqrt{3}=0$
Answer:
\begin{array}{l}
 
\begin{array}{l}
 \text{Solve the following system}: \\
 \{
\begin{array}{ll}
 -34\ 3^{-1/2} y+9 \sqrt{3} x-3 \sqrt{3}=0 & \text{    (equation }1) \\
 -3^{-1/2} y+2\ 3^{-1/2} x-14 \sqrt{3}=0 & \text{    (equation }2) \\
\end{array}
 \\
\end{array}
 \\
\hline
 
\begin{array}{l}
 \text{Express }\text{the }\text{system }\text{in }\text{standard }\text{form}: \\
 \{
\begin{array}{ll}
 9 \sqrt{3} x-\frac{34 y}{\sqrt{3}}=3 \sqrt{3} & \text{    }\text{(equation }1) \\
 \frac{2 x}{\sqrt{3}}-\frac{y}{\sqrt{3}}=14 \sqrt{3} & \text{    }\text{(equation }2) \\
\end{array}
 \\
\end{array}
 \\
 
\begin{array}{l}
 \text{Subtract }\frac{2}{27}\, \times \, (\text{equation }1) \text{from}\text{ equation }2: \\
 \{
\begin{array}{ll}
 9 \sqrt{3} x-\frac{34 y}{\sqrt{3}}=3 \sqrt{3} & \text{    }\text{(equation }1) \\
 \fbox{$0 x+\frac{41 y}{27 \sqrt{3}}=\frac{124}{3 \sqrt{3}}$} & \text{    }\text{(equation }2) \\
\end{array}
 \\
\end{array}
 \\
 
\begin{array}{l}
 \text{Multiply}\text{ equation }1 \text{by }\sqrt{3}: \\
 \{
\begin{array}{ll}
 \fbox{$27 x-34 y=9$} & \text{    }\text{(equation }1) \\
 0 x+\frac{41 y}{27 \sqrt{3}}=\frac{124}{3 \sqrt{3}} & \text{    }\text{(equation }2) \\
\end{array}
 \\
\end{array}
 \\
 
\begin{array}{l}
 \text{Multiply}\text{ equation }2 \text{by }27 \sqrt{3}: \\
 \{
\begin{array}{ll}
 27 x-34 y=9 & \text{    }\text{(equation }1) \\
 \fbox{$0 x+41 y=1116$} & \text{    }\text{(equation }2) \\
\end{array}
 \\
\end{array}
 \\
 
\begin{array}{l}
 \text{Divide}\text{ equation }2 \text{by }41: \\
 \{
\begin{array}{ll}
 27 x-34 y=9 & \text{    }\text{(equation }1) \\
 \fbox{$0 x+y=\frac{1116}{41}$} & \text{    }\text{(equation }2) \\
\end{array}
 \\
\end{array}
 \\
 
\begin{array}{l}
 \text{Add }34\, \times \, (\text{equation }2) \text{to}\text{ equation }1: \\
 \{
\begin{array}{ll}
 \fbox{$27 x+0 y=\frac{38313}{41}$} & \text{    }\text{(equation }1) \\
 0 x+y=\frac{1116}{41} & \text{    }\text{(equation }2) \\
\end{array}
 \\
\end{array}
 \\
 
\begin{array}{l}
 \text{Divide}\text{ equation }1 \text{by }27: \\
 \{
\begin{array}{ll}
 \fbox{$x+0 y=\frac{1419}{41}$} & \text{    }\text{(equation }1) \\
 0 x+y=\frac{1116}{41} & \text{    }\text{(equation }2) \\
\end{array}
 \\
\end{array}
 \\
 
\begin{array}{l}
 \text{Collect }\text{results}: \\
 \fbox{$
\begin{array}{ll}
 \text{Answer:} &  \\
 \text{} & \{
\begin{array}{l}
 x=\frac{1419}{41} \\
 y=\frac{1116}{41} \\
\end{array}
 \\
\end{array}
$} \\
\end{array}
 \\
\end{array}

{'source': 'AMPS', 'file': 'amps/mathematica/algebra/system_of_equations_w_steps/1578.txt'}