#### Answer

The equations have the same slopes, but different y-intercepts.
Therefore, the system is inconsistent, there are no solutions.

#### Work Step by Step

First equation:
$3x+7y=4$
$7y=-3x+4$
$y=-\frac{3}{7}x+\frac{4}{7}$
Second equation:
$6x+14y=3$
$14y=-6x+3$
$y=-\frac{6}{14}+3\frac{3}{14}=-\frac{3}{7}x+\frac{3}{14}$
This means that the equations have the same slopes, but different y-intercepts.
Therefore, the system is inconsistent, there are no solutions.