Given
px + qy + rz = 1
p + qx + ry = z
pz + q + rx = y
py + qz + r = x
x + y + z = -3
find p + q + r
+506 If you add the first 4 equations:
\(p+q+r+pz+py+pz+qx+qy+qz+rx+ry+rz=x+y+z+1\)
substitute x+y+z for -3:
\(p+q+r+pz+py+pz+qx+qy+qz+rx+ry+rz=-2\\(p+q+r)+p(x+y+z)+q(x+y+z)+r(x+y+z)=-2\\ (p+q+r)+(p+q+r)(x+y+z)=-2\\(p+q+r)(1+(x+y+z))=-2\)
substitute x+y+z for -3 again:
\((p+q+r)(-2)=-2\\\boxed{p+q+r=1}\)
