$\left\{\begin{array} { l } y=-3x \\ x-3y+2=0\end{array} \right.$
Substitute the given value of $y$ into the equation $x-3y+2=0$$x-3 \times \left( -3x \right)+2=0$
Solve the equation for $x$$x=-\frac{ 1 }{ 5 }$
Substitute the given value of $x$ into the equation $y=-3x$$y=-3 \times \left( -\frac{ 1 }{ 5 } \right)$
Solve the equation for $y$$y=\frac{ 3 }{ 5 }$
The possible solution of the system is the ordered pair $\left( x, y\right)$$\left( x, y\right)=\left( -\frac{ 1 }{ 5 }, \frac{ 3 }{ 5 }\right)$
Check if the given ordered pair is the solution of the system of equations$\left\{\begin{array} { l } 3 \times \left( -\frac{ 1 }{ 5 } \right)+\frac{ 3 }{ 5 }=0 \\ -\frac{ 1 }{ 5 }-3 \times \frac{ 3 }{ 5 }+2=0\end{array} \right.$
Simplify the equalities$\left\{\begin{array} { l } 0=0 \\ 0=0\end{array} \right.$
Since all of the equalities are true, the ordered pair is the solution of the system$\left( x, y\right)=\left( -\frac{ 1 }{ 5 }, \frac{ 3 }{ 5 }\right)$