Prove by induction or strong induction that every even integer $\displaystyle n$ greater than 30 can be written in the form: $\displaystyle n=6x+10y, \; \; where \; x,y \in \mathbb{Z}^{+}$

So I started off with my basis step this way:

$\displaystyle Basis \; Step: \; n=16$

$\displaystyle 2n=6x+10y$

$\displaystyle 2(16)=6\cdot2 + 10\cdot 2$

$\displaystyle 32=6\cdot2 + 10\cdot 2$

So the basis step is true.

Then follows the inductive step:

$\displaystyle Inductive \; Step: \; Assume \; 2(k+1)=6x+10y \;is \; true \; for \; k=n$

$\displaystyle 2k+2=6x+10y$

Then I realise I am stuck here. I don't know how I should move on from here. The usual inductions are like I could find something that looks like the basis step and then replace the k+1 part with the basis claim. But I can't do this in this one.

Thanks for any help.