$\left\{\begin{array} { l } -3Y=3-X \\ 2X=3Y\end{array} \right.$
Swap the sides of the equation$\left\{\begin{array} { l } -3Y=3-X \\ 3Y=2X\end{array} \right.$
Multiply both sides of the equation by $-1$$\left\{\begin{array} { l } 3Y=-3+X \\ 3Y=2X\end{array} \right.$
Since both expressions $-3+X$ and $2X$ are equal to $3Y$, set them equal to each other forming an equation in $X$$-3+X=2X$
Solve the equation for $X$$X=-3$
Substitute the given value of $X$ into the equation $3Y=2X$$3Y=2 \times \left( -3 \right)$
Solve the equation for $Y$$Y=-2$
The possible solution of the system is the ordered pair $\left( X, Y\right)$$\left( X, Y\right)=\left( -3, -2\right)$
Check if the given ordered pair is the solution of the system of equations$\left\{\begin{array} { l } -3-3 \times \left( -2 \right)=3 \\ 2 \times \left( -3 \right)=3 \times \left( -2 \right)\end{array} \right.$
Simplify the equalities$\left\{\begin{array} { l } 3=3 \\ -6=-6\end{array} \right.$
Since all of the equalities are true, the ordered pair is the solution of the system$\left( X, Y\right)=\left( -3, -2\right)$