$\left\{\begin{array} { l } 12x-6y=36 \\ 3x+6y=34\end{array} \right.$
Sum the equations vertically to eliminate at least one variable$15x=70$
Divide both sides of the equation by $15$$x=\frac{ 14 }{ 3 }$
Substitute the given value of $x$ into the equation $2x-y=6$$2 \times \frac{ 14 }{ 3 }-y=6$
Solve the equation for $y$$y=\frac{ 10 }{ 3 }$
The possible solution of the system is the ordered pair $\left( x, y\right)$$\left( x, y\right)=\left( \frac{ 14 }{ 3 }, \frac{ 10 }{ 3 }\right)$
Check if the given ordered pair is the solution of the system of equations$\left\{\begin{array} { l } 2 \times \frac{ 14 }{ 3 }-\frac{ 10 }{ 3 }=6 \\ 3 \times \frac{ 14 }{ 3 }+6 \times \frac{ 10 }{ 3 }=34\end{array} \right.$
Simplify the equalities$\left\{\begin{array} { l } 6=6 \\ 34=34\end{array} \right.$
Since all of the equalities are true, the ordered pair is the solution of the system$\left( x, y\right)=\left( \frac{ 14 }{ 3 }, \frac{ 10 }{ 3 }\right)$