The system of equations is:
p - 2q = 3 q - 2r = -2 p + r = 9
We can solve this system using Gaussian Elimination.
First, we can add the first and second equations to get:
p - 2q + q - 2r = 1
This simplifies to:
-q - 2r = 1
Now, we can subtract the third equation from this equation to get:
-q - 2r - (p + r) = 1 - 9
This simplifies to:
-2q = -8
Therefore, q = 4.
Now, we can substitute this value into the second equation to get:
4 - 2r = -2
This simplifies to:
2r = 6
Therefore, r = 3.
Finally, we can substitute these values into the first equation to get:
p - 2(4) = 3
This simplifies to:
p = 5
Therefore, the ordered triple that satisfies the system of equations is (5, 4, 3).