Algebra practice question

Answer: C. 8

A system of two linear equations has no solution when the lines are parallel, which happens when the x- and y-coefficients are proportional but the constants are not. Since 6 = 2(3), the second equation's coefficients must be twice the first's, so k = 2(4) = 8. Checking: 8x + 6y = 30 is parallel to 8x + 6y = 24, so there is no solution. Choice A comes from using the reciprocal ratio, multiplying 4 by 3/6 = 1/2. Choice B comes from simply copying the coefficient 4 from the first equation. Choice D comes from scaling by the ratio of the constants, 30/12 = 2.5, times 4.

Why the other answers are wrong

A. 2

You used the reciprocal ratio, multiplying 4 by 3/6 = 1/2. Since 6 is twice 3, the x-coefficient must also double: k = 8.

B. 4

You copied the coefficient 4 from the first equation, but that would make the y-coefficients mismatched (3 vs. 6). Scale both by 2 to get k = 8.

D. 10

You scaled 4 by the ratio of the constants, 30/12 = 2.5. Parallel lines require the coefficients to be proportional, not the constants — use 6/3 = 2, so k = 8.

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