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 )