$\left\{\begin{array} { l } 2x+3y=6 \\ -2x-2y=-8\end{array} \right.$
Sum the equations vertically to eliminate at least one variable$y=-2$
Substitute the given value of $y$ into the equation $x+y=4$$x+\left( -2 \right)=4$
Solve the equation for $x$$x=6$
The possible solution of the system is the ordered pair $\left( x, y\right)$$\left( x, y\right)=\left( 6, -2\right)$
Check if the given ordered pair is the solution of the system of equations$\left\{\begin{array} { l } 2 \times 6+3 \times \left( -2 \right)=6 \\ 6+\left( -2 \right)=4\end{array} \right.$
Simplify the equalities$\left\{\begin{array} { l } 6=6 \\ 4=4\end{array} \right.$
Since all of the equalities are true, the ordered pair is the solution of the system$\left( x, y\right)=\left( 6, -2\right)$