A. None
B. One
C. Two
D. Four
E. Infinitely many questions

Answer: A

Given 3p + q = 5,
6p = 12 – 3q – 3p ⟹9p+3q=12
Both equations are of the form A_1p+B_1q=C1 and A_2p+B_2q=C2
Find \frac{A_1}{A_2}, \frac{B_1}{B_2} and \frac{C_1}{C_2}

\frac{A_1}{A_2}=\frac{3}{9}=\frac{1}{3} \frac{B_1}{B_2}=\frac{1}{3} \frac{C_1}{C_2}=\frac{5}{12}

So, \frac{A_1}{A_2} = \frac{B_1}{B_2} \neq \frac{C_1}{C_2}
This is a condition for parallel lines. So, there is no solution.

Hence, the answer is A.


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