First, subtract 2y from the first equation. This makes:
3x=-2y-5
Next, add 5
3x+5=-2y
Finally, divide each side by two. You would do these steps because you want to find out what the slopes and y intercepts are.
-3/2x-5/2=y
y=-3/2x-5/2
Do the same thing to the other equation. You should get:
-2x+3y=-5
-2x=-3y-5
-2x+5=-3y
Finally, divide by -3 on both sides:
2/3x-5/3=y
y=2/3x-5/3
Finally, compare the two lines.
y=-3/2x-5/2
y=2/3x-5/3
The two lines are perpendicular because the slopes are total opposites from each other. One is negative and the other is positive, and the fraction on both of them is the reverse of the other. These two things are what makes the line perpendicular. For the line to be parallel, both the slopes would have to be the same thing
