$\left\{\begin{array} { l } -3x+12y=-12 \\ 3x=2y-8\end{array} \right.$
Move the variable to the left-hand side and change its sign$\left\{\begin{array} { l } -3x+12y=-12 \\ 3x-2y=-8\end{array} \right.$
Sum the equations vertically to eliminate at least one variable$10y=-20$
Divide both sides of the equation by $10$$y=-2$
Substitute the given value of $y$ into the equation $3x-2y=-8$$3x-2 \times \left( -2 \right)=-8$
Solve the equation for $x$$x=-4$
The possible solution of the system is the ordered pair $\left( x, y\right)$$\left( x, y\right)=\left( -4, -2\right)$
Check if the given ordered pair is the solution of the system of equations$\left\{\begin{array} { l } -3=3 \times \left( -2 \right)-\frac{ 3 }{ 4 } \times \left( -4 \right) \\ 3 \times \left( -4 \right)=2 \times \left( -2 \right)-8\end{array} \right.$
Simplify the equalities$\left\{\begin{array} { l } -3=-3 \\ -12=-12\end{array} \right.$
Since all of the equalities are true, the ordered pair is the solution of the system$\left( x, y\right)=\left( -4, -2\right)$