We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

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