$\left\{\begin{array} { l } 2x-3y=9 \\ 5x+3y=-30\end{array} \right.$
Sum the equations vertically to eliminate at least one variable$7x=-21$
Divide both sides of the equation by $7$$x=-3$
Substitute the given value of $x$ into the equation $2x-3y=9$$2 \times \left( -3 \right)-3y=9$
Solve the equation for $y$$y=-5$
The possible solution of the system is the ordered pair $\left( x, y\right)$$\left( x, y\right)=\left( -3, -5\right)$
Check if the given ordered pair is the solution of the system of equations$\left\{\begin{array} { l } 2 \times \left( -3 \right)-3 \times \left( -5 \right)=9 \\ -5 \times \left( -3 \right)-3 \times \left( -5 \right)=30\end{array} \right.$
Simplify the equalities$\left\{\begin{array} { l } 9=9 \\ 30=30\end{array} \right.$
Since all of the equalities are true, the ordered pair is the solution of the system$\left( x, y\right)=\left( -3, -5\right)$