[1] + [2a] gives:
31x + 0 = 62
Solving that equation gives x = 2
Now we know x, so we can substitute it into one of the original equations. Substituting x = 2 into [1] gives
6 + 4y = 26
<=> 4y = 20
<=> y = 5
We now have the pair of values, x and y, which satisfy both equations. Therefore we know that (2,5) lies on both lines, which means that it must be at the intersection of those two lines.
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In that particular example it was only necessary to multiply one of the equations to make the coefficients of one of the terms the same. Sometimes it's necessary to multiply both equations by suitable values.
Also, in that example the 'new' equations needed to be added together (in order to get a zero coefficient). If the 'new' coefficients were both positive (or both negative) you'd have to subtract one equation from the other.
Chris
(PS: I see that other have been posting while I've been typing my answer. We've all agreed on the technique but I've posted anyway, in case you need further explanation of the reasons for the operations)