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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

 Jun 7, 2023
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\(\text{We write the first equation as it is: } \space\space\space\space p-2q=3 \space\space\space\space\space\space\space\space\space\space\space (1)\)

\(\text{The second equation can be written as: } \space\space\space\space -2r=-2 \implies r=1 \space\space\space\space\space\space\space (2)\)

\(\text{The third equation can be written as: } \space\space\space\space r=9 \space\space\space\space\space\space\space\space (3)\)

Noticing that (2) and (3) say that r=1 and r=9 respectively. But this is not possible! (A contradiction)
Hence, this system of equations does not have a unique solution

 Jun 7, 2023

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