system

To find the ordered triple (p,q,r), we can use substitution:

First equation: $2q=-p$ ---> $q=-p/2$

Second equation: $-p/2-2r=0$ ---> $-p/2=2r$ ---> $p=-4r$

Third equation: $-4r+ r=5$ ---> $-3r=5$ ---> $r=-5/3$

Plugging in -5/3 for r: $q+10/3=0$ ---> $q=-10/3$

Plugging in -10/3 for q: $p-20/3=0$ ---> $p=20/3$

the ordered triple (p,q,r) is ( 20/3 , -10/3 , -5/3 )

Answer: ( 20/3 , -10/3 , -5/3 )