Question

Determine whether the systems have one solution, no solution or infinitely solutions

Answer 1

Problem would be easier to do if you'd write one function above the other:

3x-2y=3; 6x-4y=1 should be:

3x-2y=3
6x-4y=1
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Please note that if you mult. the first equation by 2, you get 6x-4y= 6, which is almost but not quite the same as the second equation.  
It should be obvious that 6x-4 in the first equation are the same expression as 6x-4 in the second equation.  6x-4 cannot = 6 and also =1 at the same time, so this system has NO solution.  The 2 lines never intersect.