Jhevon is going to kill me for that
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By the way ^^
I suppose you're in high school and because you talked about linear systems, we'll do it this way :
The equation of a plane is
So write the linear system of equations assuming that P, Q, R and S are in this plane. Then solve for a,b,c and d.
If it has a (unique) solution, it will mean that the points are coplanar I'll let you do the working, because I really have to go to bed
Actually, this is equivalent to Reckoner's method, but his is for higher grades