The pair of linear equations $kx + 2y = 5$ and $3x + y = 1$ has a unique solution if:
(a) $k = 6$
(b) $k
eq 6$
(c) $k = 0$
(d) $k
eq 0$
Step-by-Step Solution
Key Concept: Unique solution $\Rightarrow \dfrac{a_1}{a_2} <br>eq \dfrac{b_1}{b_2}$.
Here $a_1=k, b_1=2$ and $a_2=3, b_2=1$. [0.5 Mark]
$\dfrac{k}{3}
eq \dfrac{2}{1} \Rightarrow k
eq 6$. [0.5 Mark]
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🎯 Official CBSE Marking Scheme:
Unique solution ratio condition: 0.5 Mark
Deducing $k
eq 6$: 0.5 Mark
Correct Answer: $k \neq 6$