Question 114656
First of all, I'm assuming you meant a+6b=18 for the second equation.  Personally, I would subtract 6b from both sides from the second equation and then use substitution, but elimination works just as well, of course.  Either method will give you the same answer.

First, multiply the second equation by -3.  To do this, you must multiply each term by -3.  The first equation will remain unchanged:

 3a + 2b = 2
-3a - 18b = -54

Now combine (the a's will cancel out):
-16b = -52

Divide by -16:

b = {{{52/16}}}, or 3{{{4/16}}} or 3{{{1/4}}}, or 3.25.

Now, sub 3.25 for b in either equation to find a.  I'll choose the first:
3a + 2(3.25) = 2
3a + 6.5 = 2
3a = -4.5
a = -1.5

So the point of intersection of those two lines is (-1.5, 3.25).