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Pair of Linear Equations in Two Variables
RD Sharma
CBSE
Grade 10

Question:

For what value of $k$, do the equations $3x - y + 8 = 0$ and $6x - ky = -16$ represent coincident lines?
(a) $\dfrac{1}{2}$
(b) $-\dfrac{1}{2}$
(c) $2$
(d) $-2$

Step-by-Step Solution

Key Concept: $6x - ky + 16 = 0$. Coincident condition: $\\dfrac{3}{6} = \\dfrac{-1}{-k} = \\dfrac{8}{16} \Rightarrow \\dfrac{1}{2} = \\dfrac{1}{k} \Rightarrow k = 2$.
$\\dfrac{3}{6} = \\dfrac{-1}{-k} \Rightarrow \\dfrac{1}{2} = \\dfrac{1}{k} \Rightarrow k = 2$. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Solving $\\dfrac{1}{2} = \\dfrac{1}{k} \Rightarrow k = 2$: 1.0 Mark

Correct Answer: $2$
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