Algebra practice question

Answer: C. 12

Infinitely many solutions means the two equations are the same line. Multiplying the first by 2 gives 4x + 6y = 12, so k = 12. If k were anything else, the lines would be parallel with no solution.

Why the other answers are wrong

A. 3

You divided 6 by 2 instead of multiplying; the first equation must be scaled up by 2 to match 4x + 6y, so k = 6 × 2.

B. 6

You kept the original constant, but the second equation's coefficients are doubled, so the constant must be doubled too: k = 12.

D. 18

Multiplying 6 by 3 doesn't match the coefficients — 2x + 3y becomes 4x + 6y when multiplied by 2, not 3, so k = 12.

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