Eliminate either one of the two letters.
I'll arbitrarily pick "b" to eliminate,
in order to solve for b.  However I
could have picked "a" to eliminate in
order to solve for "b" just as well.  

Multiplying the 1st equation by -2 will
cause its "b"-term to become -2b and then
it will cancel with the +2b in the 2nd
equation when we add them term-by-term:

------------------------



Divide both sides by -3, the coefficient of "a":



   

Since "a" came out to be a simple number like 6, and not
some terrible fraction like , it's easier to finish
by switching over to the substitution method to find b:

Substitute a = 6 in either one of the two original equation.
I'll pick the first one, only because it has the simpler
coefficient for "b":





   

[Note: If "a" had come out to be some terrible fraction 
like , and it WILL once in a while, then you
wouldn't switch over to substitution.  Instead you would
start over and eliminate "a" to find "b".]

Edwin