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Luv2Teach
Solve the second equation for x.  x = 2y - 8.  Now sub this into the first equation to get [tex]3(2y-8)-6y=-12[/tex], and simplifying you will get 6y - 24 - 6y = -12.  6y - 6y eliminates the term, leaving us with -24 = -12, which of course is an untrue statement.  This is what we refer to as an inconsistent system.  These 2 lines, when solved for y give us the same slope.  That is why there is no solution.  A solution exists where the lines intersect.  Lines with identical slopes do not intersect.  What we know about the 2 lines is that they are parallel.
AL2006
(a).
IF you were to solve the first equation for 'y', you'd get  Y = x/2 + 4 .
and
IF you were to solve the second equation for 'y', you'd get  Y = x/2 + 2 .

Well, look.  If those two quantities are both equal to 'y',
then they must be equal to each other, so we can write  x/2 + 4  =  x/2 + 2 .

Subtract  x/2  from each side:  4 = 2 .

Is there any value of 'x' that can make 4 equal to 2 ?
No.  There is no value of 'x' that can make 4 equal to 2 .

This tells us that (x/2 + 4) can never be equal to (x/2 + 2) .

And THAT tells us that the original two equations (that these came from)
can't both be equal at the same time ... another way of saying that the
pair has no solution.

(b).
Do you remember what you learned about (Y = mx + b) ?
The slope and the intercept and all that stuff ?

Great ! 
Then you remember that the slope of (Y = x/2 + 4) is 1/2,
AND the slope of (Y = x/2 + 2) is also 1/2 .

The original two equations both have the same slope.
Their graphs are PARALLEL lines ! 
THAT's why they have no solution.
Because parallel lines never intersect.

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