Let G be $\displaystyle R^2$ , H={$\displaystyle (t,3t) : t\in R$}.

I need to find the left cosets of G for the subgroup H. (describe it)

For every 't' I choose, there's still many options left, and there's not any 'bunch' of t's I can choose that will cover all the options (options=G, when I think of it).

How can I still explain this, in a mathematical way? Or, IS there any way to define the cosets?

Thanks