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

p - 2q = 3

q - 2r = -2 + q

p + r = 9 + p

 May 16, 2023
 #1
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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 \(-2r = -2 \rightarrow r=1.\) Subtracting $p$ from both sides in the last equation yields \(r=9,\) contradiction, so the system does not have a solution \((p,q,r).\)

 May 16, 2023

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