You can put this solution on YOUR website! You need to compare the slopes, if slopes are the same then they're parallel. So what you do is solve each equation for y and put it in slope intercept form which is y=mx+b where m is your slope.
3y=-2x+1
2y=-3x+10
Divide first equation by 3 and second one by 2 and you get
So the slopes are -2/3 and -3/2, they're NOT the same so the lines are NOT parallel.