$\left\{\begin{array} { l } 4x-5y=18 \\ 6x+10y=-78\end{array} \right.$
Convert the augmented matrix into a system of linear equations$\left\{\begin{array} { l } y=-6 \\ x=-3\end{array} \right.$
The possible solution of the system is the ordered pair $\left( x, y\right)$$\left( x, y\right)=\left( -3, -6\right)$
Check if the given ordered pair is the solution of the system of equations$\left\{\begin{array} { l } 4 \times \left( -3 \right)-5 \times \left( -6 \right)=18 \\ 6 \times \left( -3 \right)+10 \times \left( -6 \right)=-78\end{array} \right.$
Simplify the equalities$\left\{\begin{array} { l } 18=18 \\ -78=-78\end{array} \right.$
Since all of the equalities are true, the ordered pair is the solution of the system$\left( x, y\right)=\left( -3, -6\right)$