Correct Answer:
Option C —
m ≠ 6
The two equations are:
5a + 7b = 2
15a + 21b = m
Notice that the second equation is exactly 3 times the first equation (coefficients: 5×3=15, 7×3=21).
If m = 3 × 2 = 6, the second equation is identical to the first (just multiplied by 3) → the system has infinitely many solutions.
If m ≠ 6, the two equations represent parallel lines (same slope but different intercepts) → the system has no solution (zero solutions).
Therefore, the equations have zero solution when m ≠ 6.
Correct answer: C) m ≠ 6
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
