$\left\{\begin{array} { l } -3x-6y=-39 \\ 3x-5y=6\end{array} \right.$
Sum the equations vertically to eliminate at least one variable$-11y=-33$
Divide both sides of the equation by $-11$$y=3$
Substitute the given value of $y$ into the equation $3x-5y=6$$3x-5 \times 3=6$
Solve the equation for $x$$x=7$
The possible solution of the system is the ordered pair $\left( x, y\right)$$\left( x, y\right)=\left( 7, 3\right)$
Check if the given ordered pair is the solution of the system of equations$\left\{\begin{array} { l } 7+2 \times 3=13 \\ 3 \times 7-5 \times 3=6\end{array} \right.$
Simplify the equalities$\left\{\begin{array} { l } 13=13 \\ 6=6\end{array} \right.$
Since all of the equalities are true, the ordered pair is the solution of the system$\left( x, y\right)=\left( 7, 3\right)$