Q1. [1] § 3.2 Graphical Method of Solution of a Pair of Linear Equations § 3.4 Summary
Directions: Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.
Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.
- (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
- (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
- (C) Assertion (A) is true, but Reason (R) is false.
- (D) Assertion (A) is false, but Reason (R) is true.
Previously asked in CBSE board exam
2026 30/5/1 Q19
Generated by claude-sonnet-4-6 · 2026-06-15 10:35 · grounding rag
Model Answer
(C) Assertion (A) is true, but Reason (R) is false.
For the given equations: $\frac{3}{-6} = \frac{-5}{10} = \frac{1}{2}$, but $\frac{7}{14} = \frac{1}{2}$... wait — $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$ (since $\frac{7}{14} \neq \frac{-5}{10}$... rechecking: $\frac{3}{-6}=\frac{-1}{2}$, $\frac{-5}{10}=\frac{-1}{2}$, $\frac{7}{14}=\frac{1}{2}$), so the system is inconsistent — A is true. But R is false because when there is no unique solution, lines can be parallel (no solution) or coincident (infinitely many solutions) — not always parallel.
(C)
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Explanation
- Assertion is true: $\frac{a_1}{a_2}=\frac{-1}{2},\ \frac{b_1}{b_2}=\frac{-1}{2},\ \frac{c_1}{c_2}=\frac{7}{14}=\frac{1}{2}$; since $\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}$, the pair is inconsistent (parallel lines). ✓
- Reason is false: "no unique solution" includes both parallel lines (no solution) and coincident lines (infinitely many solutions). Parallel lines are only one case; coincident lines also lack a unique solution. So R is an incorrect generalisation.
- Examiner looks for correct identification of the flaw in R and verification of A using ratio comparison.
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