I know how to use the elimination method - just that I can't quite figure it out on these type of linear systems: $$ \begin{array}{ccc} y &=& –\frac{5}{3}x + 3 \\ y &=& \frac{1}{3}x - 3 \end{array} $$
They do line up perfectly, so does this mean it becomes: $ 0 = \dfrac{-4x}{3} $??
Looks like you added the equations since the 3's cancelled. Then left side is $2y$ not $0.$ Try subtracting instead.