$\left\{\begin{array} { l } -6y=4-4x \\ 5x-6y=2\end{array} \right.$
Move the variable to the right-hand side and change its sign$\left\{\begin{array} { l } -6y=4-4x \\ -6y=2-5x\end{array} \right.$
Since both expressions $4-4x$ and $2-5x$ are equal to $-6y$, set them equal to each other forming an equation in $x$$4-4x=2-5x$
Solve the equation for $x$$x=-2$
Substitute the given value of $x$ into the equation $-6y=2-5x$$-6y=2-5 \times \left( -2 \right)$
Solve the equation for $y$$y=-2$
The possible solution of the system is the ordered pair $\left( x, y\right)$$\left( x, y\right)=\left( -2, -2\right)$
Check if the given ordered pair is the solution of the system of equations$\left\{\begin{array} { l } 4 \times \left( -2 \right)-6 \times \left( -2 \right)=4 \\ 5 \times \left( -2 \right)-6 \times \left( -2 \right)=2\end{array} \right.$
Simplify the equalities$\left\{\begin{array} { l } 4=4 \\ 2=2\end{array} \right.$
Since all of the equalities are true, the ordered pair is the solution of the system$\left( x, y\right)=\left( -2, -2\right)$