Does every regular language have a linear grammar? Some definitions and facts (from Wikipedia):


A linear grammar is a context-free grammar that has at most one nonterminal in the right hand side of each of its productions.
the left-linear or left regular grammars, in which all nonterminals in right hand sides are at the left ends;
the right-linear or right regular grammars, in which all nonterminals in right hand sides are at the right ends.
Collectively, these two special types of linear grammars are known as the regular grammars; both can describe exactly the regular languages.


Doubts


Fourth fact used word "collectively" and then "both". What does it actually mean? 


there is both right linear and left linear grammar for all regular languages
there is either right linear or left linear grammar for all regular languages  

Can all non-linear regular grammars be converted into linear regular grammars? (Is there any systematic procedure for that?)


Update

I got it now how we can translate RLG to LLG and vice versa. So any given regular language has both RLG and LLG. Now the second question is remaining: Can all non-linear regular grammars be converted into linear regular grammars?
Answer to the last question of the update.

The grammar $S \to aSb + 1$ is linear, but it generates the nonregular language $\{a^nb^n \mid n \geqslant 0\}$. Therefore, it cannot be converted into a regular linear grammar.