Find the ordered triple (p,q,r) that satisfies the following system:

p - 2q = 3

q - 2r = -2 + q

p + r = 9 + p

cooIcooIcooI17 Sep 24, 2024

#1**+1 **

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)**.

nerdboy Sep 24, 2024