Find the ordered triple (p,q,r) that satisfies the following system:
p - 2q = 3
q - 2r = -2 + q
p + r = 9 + p
+42 I claim that the system of equations has no solutions. Assume, for the sake of contradiction, that the equation does have solutions. Subtracting q from both sides in the second equation yields −2r=−2→r=1. Subtracting p from both sides in the last equation yields r=9, contradiction, so the system does not have a solution (p,q,r).
