system

To solve this system, we can use algebraic manipulation to eliminate variables and solve for one variable in terms of the others.

First, let's simplify the second equation by moving the q term to the left-hand side:

q - 2r - q = -2

Simplifying, we get:

-q - 2r = -2

Now we can eliminate q by adding the first equation to this simplified second equation:

(p - 2q) + (-q - 2r) = 3 - 2

Simplifying, we get:

p - 3q - 2r = 1

Next, we can use the third equation to eliminate r by solving for p in terms of r and substituting into the third equation:

p + r = 9 + p

Subtracting p from both sides, we get:

r = 9

Now we can substitute this value of r into the equation we just derived:

p - 3q - 2r = 1

p - 3q - 2(9) = 1

Simplifying, we get:

p - 3q = 19

Finally, we can use the first equation to solve for p in terms of q:

p - 2q = 3

p = 2q + 3

Substituting this expression for p into the equation we just derived, we get:

(2q + 3) - 3q = 19

Simplifying, we get:

-q = 16

Dividing both sides by -1, we get:

q = -16

Now we can use the expression we derived earlier to solve for p:

p = 2q + 3 = 2(-16) + 3 = -29

Therefore, the ordered triple that satisfies the system is (-29, -16, 9).