Question

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

p - 2q = 3

q - 2r = -2 + q

p + r = 9 + p

Answer 1

We can start by simplifying the second equation:

q - 2r = -2 + q

Subtracting q from both sides, we get:

-2r = -2

Dividing by -2, we get:

r = 1

Now we can substitute r = 1 into the third equation:

p + r = 9 + p

p + 1 = 9 + p

Subtracting p from both sides, we get:

1 = 9

This is a contradiction, so there are no solutions to the system. Therefore, there is no ordered triple that satisfies the given equations.