Determine whether the pair of equations $3x+2y=7$ and $6x+4y=20$ are consistent, inconsistent, or represent the same straight line. Justify your answer.

Step-by-step solution

1. Write the two equations: (1) 3x + 2y = 7, (2) 6x + 4y = 20.
2. Observe that the coefficients of (2) are exactly twice those of (1): 6 = 2·3 and 4 = 2·2.
3. If the constant term also doubled, the lines would be the same. Double of 7 is 14, but the constant in (2) is 20, not 14.
4. Since the left‑hand sides are proportional but the right‑hand sides are not, the two lines are parallel and distinct.
5. Parallel distinct lines have no common point, therefore the system is inconsistent.

Concept tested: Consistency of linear systems

Published 24 August 2026 · How this solution was prepared and checked

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