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Pair of Linear Equations in Two Variables
RD Sharma
CBSE
Grade 10
Question:
A pair of linear equations $a_1 x + b_1 y + c_1 = 0$ and $a_2 x + b_2 y + c_2 = 0$ has no solution if: (a) $\dfrac{a_1}{a_2} eq \dfrac{b_1}{b_2}$ (b) $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2}$ (c) $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} eq \dfrac{c_1}{c_2}$ (d) $\dfrac{a_1}{a_2} eq \dfrac{c_1}{c_2}$
Step-by-Step Solution
Key Concept: Parallel lines condition.
No solution corresponds to parallel lines, which occurs when $a_1/a_2 = b_1/b_2 eq c_1/c_2$. [1.0 Mark]
--- 🎯 Official CBSE Marking Scheme: Selecting parallel lines condition: 1.0 Mark