+128475 p + q + r = -3
px + qy + rz = 1
p + qx + ry = z
pz + q + rx = y
py + qz + r = x
Add the last three equations and we get that
(p + q + r) + ( q + r)x + (p + r)y + (p + q)z = x + y + z
-3 + (q + r)x + (p + r)y + (p + q)z = x + y + z
Manipulating the first equation and substituting we have
-3 + (-3-p)x + (-3 -q)y + (-3 -r)z = x + y + z
-3 + -3x - px + -3y -qy + -3z - rz = x + y + z rearrange as
-3 - px - qy - rz = x + 3x + y + 3y + z + 3z
-3 - ( px + qy + rz) = 4x + 4y + 4z
-3 - (1) = 4 ( x + y + z)
-2 = 4 ( x + y + z) divide both sides by 4
-2/4 = x + y + z
-1/2 = x + y + z
