Find the ordered triple\((p, q, r)\) that satisfies the following system:
\(\begin{align*} p-2q&=0\\ q-2r&=0\\ p+r&=5. \end{align*}\)
+2666 From the first equation and second equations, we have \(p = 2q\) and \(q = 2r\), meaning \(p = 2 \times 2r = 4r\)
Substituting this into the third equation gives us \(r = 1\). Plugging this value into the second equation gives us \(q - 2 = 0\), meaning \(q = 2\)
Finally, substituting \(q = 2\) into the first equation \(p - 4 = 0 \), meaning \(p = 4\)
So, the solution is \(\color{brown}\boxed{(4,2,1)}\)
