$\left\{\begin{array} { l } x+2y=4 \\ y-3x=2\end{array} \right.$
Use the commutative property to reorder the terms$\left\{\begin{array} { l } x+2y=4 \\ -3x+y=2\end{array} \right.$
Multiply both sides of the equation by $3$$\left\{\begin{array} { l } 3x+6y=12 \\ -3x+y=2\end{array} \right.$
Sum the equations vertically to eliminate at least one variable$7y=14$
Divide both sides of the equation by $7$$y=2$
Substitute the given value of $y$ into the equation $-3x+y=2$$-3x+2=2$
Solve the equation for $x$$x=0$
The possible solution of the system is the ordered pair $\left( x, y\right)$$\left( x, y\right)=\left( 0, 2\right)$
Check if the given ordered pair is the solution of the system of equations$\left\{\begin{array} { l } 2 \times 2+0=4 \\ 2-3 \times 0=2\end{array} \right.$
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$\left( x, y\right)=\left( 0, 2\right)$