$\left\{\begin{array} { l } 2x-3y=-18 \\ \frac{ x }{ 6 }+\frac{ y }{ 5 }=3\end{array} \right.$
Multiply both sides of the equation by $30$$\left\{\begin{array} { l } 2x-3y=-18 \\ 5x+6y=90\end{array} \right.$
Multiply both sides of the equation by $2$$\left\{\begin{array} { l } 4x-6y=-36 \\ 5x+6y=90\end{array} \right.$
Sum the equations vertically to eliminate at least one variable$9x=54$
Divide both sides of the equation by $9$$x=6$
Substitute the given value of $x$ into the equation $2x-3y=-18$$2 \times 6-3y=-18$
Solve the equation for $y$$y=10$
The possible solution of the system is the ordered pair $\left( x, y\right)$$\left( x, y\right)=\left( 6, 10\right)$
Check if the given ordered pair is the solution of the system of equations$\left\{\begin{array} { l } \frac{ 6 }{ 3 }-\frac{ 10 }{ 2 }=-3 \\ \frac{ 6 }{ 6 }+\frac{ 10 }{ 5 }=3\end{array} \right.$
Simplify the equalities$\left\{\begin{array} { l } -3=-3 \\ 3=3\end{array} \right.$
Since all of the equalities are true, the ordered pair is the solution of the system$\left( x, y\right)=\left( 6, 10\right)$