$\left\{\begin{array} { l } 5x+3y=-12 \\ 3y=-9-4x\end{array} \right.$
Substitute the given value of $3y$ into the equation $5x+3y=-12$$5x-9-4x=-12$
Solve the equation for $x$$x=-3$
Substitute the given value of $x$ into the equation $3y=-9-4x$$3y=-9-4 \times \left( -3 \right)$
Solve the equation for $y$$y=1$
The possible solution of the system is the ordered pair $\left( x, y\right)$$\left( x, y\right)=\left( -3, 1\right)$
Check if the given ordered pair is the solution of the system of equations$\left\{\begin{array} { l } 5 \times \left( -3 \right)+3 \times 1=-12 \\ 4 \times \left( -3 \right)+3 \times 1=-9\end{array} \right.$
Simplify the equalities$\left\{\begin{array} { l } -12=-12 \\ -9=-9\end{array} \right.$
Since all of the equalities are true, the ordered pair is the solution of the system$\left( x, y\right)=\left( -3, 1\right)$