#### Answer

The equations have the same slopes, and the same y-intercepts.
Therefore, the equations are dependent, there is infinite solutions.

#### Work Step by Step

First equation:
$2x=-3y+1$
$3y=-2x+1$
$y=-\frac{2}{3}x+\frac{1}{3}$
Second equation:
$6x=-9y+3$
$9y=-6x+3$
$y=-\frac{6}{9}x+\frac{3}{9}=-\frac{2}{3}x+\frac{1}{3}$
This means that the equations have the same slopes, and the same y-intercepts.
Therefore, the equations are dependent, there is infinite solutions.