Q1. [1] § 3.2 Graphical Method of Solution of a Pair of Linear Equations
The value of $k$ for which the system of equations $3x - y + 8 = 0$ and $6x - ky + 16 = 0$ has infinitely many solutions, is
- (A) $-2$
- (B) $2$
- (C) $\frac{1}{2}$
- (D) $-\frac{1}{2}$
Previously asked in CBSE board exam
2024 30/2/1 Q1
Generated by claude-sonnet-4-6 · 2026-06-15 10:32 · grounding rag
Model Answer
(B) 2
For infinitely many solutions: $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2}$. Here, $\dfrac{3}{6} = \dfrac{-1}{-k} = \dfrac{8}{16}$, giving $\dfrac{1}{2} = \dfrac{1}{k}$, so $k = 2$.
Explanation
For coincident lines (infinitely many solutions), all three ratios must be equal. Comparing $\frac{3}{6} = \frac{1}{2}$ with $\frac{-1}{-k} = \frac{1}{k}$, set $\frac{1}{k} = \frac{1}{2}$ → $k = 2$. Always check all three ratios to confirm consistency.
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