Practise 6 selected Pair of Linear Equations in Two Variables Assertion–Reason questions from CBSE Class 10 previous-year board papers (2023–2026). Check each statement, then decide whether the Reason explains the Assertion. Two true statements do not always form a correct explanation.
6 distinct questions · 18 verified board-paper appearances Solutions prepared by Team TutorVertex · Last checked: 25 October 2026
Selected board years: 2023–2026 · Basic and Standard · Consistency, solution counts and parameter conditions.
How to solve Assertion–Reason questions
In the official 2026–27 CBSE Class 10 Mathematics sample-paper format, Section A contains two Assertion–Reason questions worth one mark each across the whole paper. Basic format · Standard format.
Check whether the Assertion is true.
Check whether the Reason is true, separately.
If both are true, decide whether the Reason explains the Assertion.
Match your conclusion to the printed answer choices.
Decision table for the standard choices used below
Official CBSE answer · Explanation by Team TutorVertex
Assertion: True. Multiply the first equation by 2 and add the second: 28 = 0, a contradiction. Thus there is no common solution.
Reason: False. A pair without a unique solution may represent distinct parallel lines or coincident lines; coincident lines give infinitely many solutions.
Link: A is true and R is false. Absence of a unique solution does not by itself distinguish the two cases. Answer: C.
Consistency and coefficient conditions
Key results
For a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, unequal ratios a₁/a₂ and b₁/b₂ give a unique solution.
Where the ratios are defined: a₁/a₂ = b₁/b₂ ≠ c₁/c₂ gives no solution, while equality of all three gives infinitely many.
If a denominator is zero, do not divide by it. Compare the equations directly or use elimination.
Question 3 · Basic
Assertion (A): The system of linear equations 3x + 5y − 4 = 0 and 15x + 25y − 25 = 0 is inconsistent.
Reason (R): The pair of linear equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 is inconsistent if = ≠ .
Official CBSE answer · Explanation by Team TutorVertex
Assertion: True. Here = = , whereas = . The coefficient ratios agree but differ from the constant ratio.
Reason: True. When the displayed ratios are defined, equal x- and y-coefficient ratios with a different constant ratio describe distinct parallel lines and no common solution.
Link: The given equations satisfy the condition in R, so R explains their inconsistency. Answer: A.
Question 4 · Basic
Assertion (A): The pair of linear equations 5x + 2y + 6 = 0 and 7x + 6y + 18 = 0 have infinitely many solutions.
Reason (R): The pair of linear equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 have infinitely many solutions, if = = .
Official CBSE answer · Explanation by Team TutorVertex
Assertion: False. ≠ = , so the pair has a unique solution. Subtracting three times the first equation from the second gives −8x = 0; hence x = 0 and y = −3.
Reason: True. When the displayed ratios are defined and equal, the equations represent the same line and have infinitely many common solutions.
Link: The given pair does not satisfy the equal-ratio condition. A is false and R is true. Answer: D.
Parameter questions
Key results
Substitute the proposed parameter value and compare the whole equations, including the constants.
Equal x- and y-coefficient ratios alone do not guarantee coincident lines. The constants must have the same proportion.
Question 5 · Basic
Assertion (A): The value of p for which the system of equations 4x + py + 8 = 0 and 2x + 2y + 2 = 0 is consistent is 4.
Reason (R): The system of equations a₁x + b₁y = c₁ and a₂x + b₂y = c₂ is consistent with infinitely many solutions, if = = .
Official CBSE answer · Explanation by Team TutorVertex
Assertion: False. For p = 4, subtracting twice the second equation from the first gives 4 = 0. Thus p = 4 makes the pair inconsistent. For p ≠ 4, ≠ , so there is a unique solution and the pair is consistent.
Reason: True. With defined equal coefficient and constant ratios, one equation is a multiple of the other and the lines coincide.
Link: The stated value p = 4 gives no solution, while R correctly describes the infinitely-many-solutions case. Hence A is false and R is true. Answer: D.
Question 6 · Standard
Assertion (A): The pair of linear equations px + 3y + 59 = 0 and 2x + 6y + 118 = 0 will have infinitely many solutions if p = 1.
Reason (R): If the pair of linear equations px + 3y + 19 = 0 and 2x + 6y + 157 = 0 has a unique solution, then p ≠ 1.
Official CBSE answer · Explanation by Team TutorVertex
Assertion: True. For p = 1, twice the first equation is 2x + 6y + 118 = 0, exactly the second equation. The lines coincide.
Reason: True. The second pair has a unique solution when ≠ , which gives p ≠ 1.
Link: R concerns a different pair with constants 19 and 157. It does not establish the proportional constants 59 and 118 in A, so it does not explain A. Answer: B.
Common questions
What does a consistent pair of linear equations mean?
It has at least one common solution. Intersecting lines give one solution and coincident lines give infinitely many.
Does “not a unique solution” always mean parallel lines?
No. The lines may be distinct and parallel, giving no solution, or coincident, giving infinitely many solutions.
Do y = x and y = 2x have infinitely many solutions?
No. Equating x and 2x gives x = 0 and y = 0. Their only common solution is (0, 0).
What if a denominator in a coefficient ratio is zero?
Do not use an undefined ratio. Inspect the equations directly or eliminate a variable to decide whether they agree, contradict each other or give one solution.
How many Assertion–Reason questions come in the CBSE Class 10 Maths board paper?
The official 2026–27 Basic and Standard sample-paper format has two Assertion–Reason questions in Section A, worth one mark each across the whole paper. This does not promise a question from every chapter.
What if both statements seem false?
None of the four standard choices used here represents both statements being false. Recheck the wording, conditions and calculations, then flag a possible source or transcription error if needed.
Official sources and marking schemes
Source labels identify the original paper, set and question number. ZIP links open official archives containing the named paper.
Choices shown as in 430/7/1, Q19. The meanings and A–D order are the same in the listed appearances; layout, capitalisation and punctuation may differ.
Choices shown as in 430/1/1, Q20. The meanings and A–D order are the same in the listed appearances; layout, capitalisation and punctuation may differ.
Choices shown as in 430/4/1, Q19. The meanings and A–D order are the same in the listed appearances; layout, capitalisation and punctuation may differ.
Choices shown as in 430/1/1, Q20. The meanings and A–D order are the same in the listed appearances; layout, capitalisation and punctuation may differ.
This selection contains 6 distinct questions across 18 verified board-paper appearances from 2023–2026, including the 2026 second board examination. Exact repeats are merged. Original question numbers, sets and the A–D order are checked against each paper and its corresponding marking scheme; answers are matched by question content as well as number.
Explanations are written by Team TutorVertex in three parts: Assertion, Reason and Link. Working uses substitution, elimination and coefficient conditions within the applicable CBSE syllabus. Ratio conditions are used only where defined. No distractor explanation blocks are added.
Available official board archives and Basic and Standard sample papers for sessions 2022–23 through 2026–27 were screened. No chapter-specific Assertion–Reason item was identified in those screened sample papers, so none is counted as scored sample-paper practice. This is a selection, not a claim to every language edition or repeated appearance.
The selected questions supply no graph or data table. Nearby figures belonging to other questions have not been included. Ordinary MCQs and questions from other chapters remain separate.