Given \(\begin{align*} px+qy+rz&=1,\\ p+qx+ry&=z,\\ pz+q+rx&=y,\\ py+qz+r&=x,\\ p+q+r&=-3, \end{align*} \) find x+y+z.

Lightning
Sep 9, 2018

#1**+1 **

Best Answer

Add up the first four equations and simplify:

p(x+y+z) + p + q(x+y+z) + q + r(x+y+z) + r = 1 + x+y+z

Simplify further:

(p+q+r)(x+y+z) + p+q+r = 1 + x+y+z

Knowing that p+q+r = -3 we can write the above as

-3(x+y+z) - 3 = 1 + x+y+z

Rearranging, we have

-4 = 4(x+y+z) or x+y+z = -1

Alan
Sep 9, 2018