System

p + 2q = 0

q - 2r = 0

p + r = 5            multiply by 2     2p+2r=10    add to second equation to get

q +2p = 10      multiply by -2      -2q-4p= -20   add to top equation

-3p = -20      p = 20/3        then r = - 5/3   (from third equation)      and q = ________    (you can finish !)