Hi,
You already did some of the work. If we take your second equation and multiply it by 4 we get;
8p+8q-4r=0
and if we combine this with the last equation we have these two equations:
8p+8q-4r=0
8p+8q+4r=0
Adding these two we get:
16p+16q=0
so it becomes obvious that p and q must be negatives of each other, so pick a value for p and make q the negative of it. That should be any constant including zero.
That leaves r.
For the first equation we have:
4p+4q-2r=0
or with the above assumption we would have:
4k+4(-k)-2r=0
or simplified:
4k-4k-2r=0
which simplifies more to:
-2r=0
or simplified:
r=0
So it looks like if we call p K then we can call q -K and r=0.