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. Select the correct answer from the codes (A), (B), (C) and (D) given below. (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.

MathsCBSE Class 10 · Standard · Board exam 2025, set 30/2/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Standard 2025: question 20

Set in the CBSE Class 10 board exam of 2025, paper 30/2/1, section A, question 20, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q20 · 1 mark · Assertion-reasonCompetency-basedPair of Linear Equations in Two Variables

Assertion (A): The pair of linear equations $p x + 3 y + 59 = 0$ and $2 x + 6 y + 118 = 0$ will have infinitely many solutions if $p = 1$ .

Reason (R): If the pair of linear equations $p x + 3 y + 19 = 0$ and $2 x + 6 y + 157 = 0$ has a unique solution, then $p \neq = 1$ .

Select the correct answer from the codes (A), (B), (C) and (D) given below.

(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.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/2/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Infinitely many solutions: $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} = \frac{c _{1}}{c _{2}}$ . Unique solution: $\frac{a _{1}}{a _{2}} \neq = \frac{b _{1}}{b _{2}}$ .

Hint 2

Check each statement separately, then ask whether R explains A.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

Assertion: for infinitely many solutions, $\frac{p}{2} = \frac{3}{6} = \frac{59}{118} = \frac{1}{2}$ . This gives $p = 1$ , so A is true.
½ mark
Reason: a unique solution needs $\frac{p}{2} \neq = \frac{3}{6}$ , so $p \neq = 1$ . R is true. But R is about a different pair of equations and a different condition, so it does not explain A. Option (B).
½ mark

Answer: Option (B)

Where the marks are

Shows both A and R are true using the ratio conditions, and that R does not explain A, option (B) (1 mark)

Revise the chapter

Chapter: Pair of Linear Equations in Two Variables (notes, formulas, where marks are lost and every past question)
Topic: Graphical Method of Solving Linear Equations

Practise this chapterBoard-style questions from Pair of Linear Equations in Two Variables, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 30/2/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 20

Hints

Step-by-step solution

Revise the chapter

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