For what value of $k$ do the equations $3x+4y=12$ and $6x+8y=k$ represent the same straight line?

Step-by-step solution

1. Observe that the left‑hand side of the second equation is exactly twice the left‑hand side of the first: $6x+8y=2(3x+4y)$.
2. For two equations to represent the same line, their right‑hand sides must also be related by the same factor.
3. Multiply the right‑hand side of the first equation by 2: $2\times 12=24$.
4. Hence $k$ must be $24$ for the second equation to be identical to the first.

Concept tested: Condition for coincident lines

Published 21 August 2026 · How this solution was prepared and checked

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