Algebra practice question

Answer: A. −6

No solution means the lines are parallel: equal slopes, different intercepts. Scaling the first equation by 3 gives 9x − 6y = 24, so matching coefficients requires c = −6 (and 24 ≠ 5 confirms no solution). Choice D (6) uses the wrong sign on the y-coefficient.

Why the other answers are wrong

B. −3

You got the scale factor right (9 ÷ 3 = 3) but then attached it to the wrong number — you need to multiply the −2 by 3, giving c = −6, not just carry over the 3 with a minus sign.

C. 3

That's the scale factor between the equations (9 ÷ 3 = 3), not the new y-coefficient. Multiply the entire first equation by 3: 3x − 2y = 8 becomes 9x − 6y = 24, so c = −6.

D. 6

You found the right magnitude but lost the sign: 3 × (−2) = −6, not +6.

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