Reducing augmented matrices

Hi

How does one tell R that one is using an augmented matrix as appose to an
non-augmented matrix? 

For instance, when I want to solve two equations in two unknowns, I will
have to solve a 2 by 3 augmented matrix, however all I know to type into R
is something like this;

weights = c(1,2,3,4,5,6) (say)

M1=matrix(weights,ncol=3).

Does R correctly interpret me when I write the above code?

Furthermore, how do I reduce this augmented matrix in R such that it will
give me my two unknown variables?

Thanks so much.