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Janie was solving a system of equations and arrived at the wrong answer. Her work is shown below. Find the mistake and state how to correctly work the problem.
\(\left\{ \begin{array}{c} 3x+y=5 \\ x-y=7 \end{array} \right.\)
\(y=5-3x\)
\(x-5-3x=7\)
\(-2x-5=7\)
\(-2x=12\)
\(x=-6\)
\(y=5-3x=5-3\left(-6\right)=23\)
\(\left(-6,\ 23\right)\)
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