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UKMT Intermediate Mathematical Challenge, 2021

Algebra Difficulty 2.0 Junior Find the answer United Kingdom

Two straight lines have equations $y = px + 4$ and $py = qx - 7$ , where $p$ and $q$ are constants. The two lines meet at the point $(3, 1)$ . What is the value of $q$ ?

(A) $1$ (B) $2$ (C) $3$ (D) $4$ (E) $5$

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