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Algebra Difficulty 2.0 Junior Find the answer United Kingdom

The lines $y=x$ and $y=mx-4$ intersect at the point $P$ . What is the sum of the positive integer values of $m$ for which the coordinates of $P$ are also positive integers?

(A) $3$ (B) $5$ (C) $7$ (D) $8$ (E) $10$

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