How do you solve a system like this?
Find the ordered triple (p,q,r) that satisfies the following system:
\begin{align*}
p - 2q &= 3
q - 2r &= -2 + q
p + r &= 9 + p
\end{align*}
p = 3 + 2q
r = 9 + p - p
r = 9
q = -2 + q - 2r
0 = -2 + -2r
2 = -2r
r = -1
There are 2 different r values , thus there is no solution to this system