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 a_1x + b_1y = c_1 and a_2x + b_2y = c_2 is consistent with infinitely many solutions, if (a_1)/(a_2) = (b_1)/(b_2) = (c_1)/(c_2). Select the correct answer from the codes (A), (B), (C) and (D) as given in Questions 19 and 20. (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A). (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of 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 · Basic · Board exam 2026, set 430/1/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Basic 2026: question 20

Set in the CBSE Class 10 board exam of 2026, paper 430/1/1, 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 value of $p$ for which the system of equations $4 x + p y + 8 = 0$ and $2 x + 2 y + 2 = 0$ is consistent is $4$ .

Reason (R): The system of equations $a_{1} x + b_{1} y = c_{1}$ and $a_{2} x + b_{2} y = c_{2}$ is consistent with infinitely many solutions, if $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} = \frac{c _{1}}{c _{2}}$ .

Select the correct answer from the codes (A), (B), (C) and (D) as given in Questions 19 and 20.

(A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of 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 2026 board paper, set 430/1/1.

Hints

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

Hint 1

Substitute p = 4 and compare the three ratios.

Hint 2

Equal first two ratios but a different third ratio means what?

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.

For $p = 4$ : $\frac{a _{1}}{a _{2}} = 2$ , $\frac{b _{1}}{b _{2}} = \frac{4}{2} = 2$ , $\frac{c _{1}}{c _{2}} = \frac{8}{2} = 4$ . Since $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} \neq = \frac{c _{1}}{c _{2}}$ , the system is inconsistent, so A is false.
½ mark
R is the standard condition for infinitely many solutions, so R is true.
½ mark

Answer: Option (D)

Where the marks are

Shows the system is inconsistent at $p = 4$ , so A is false (½ mark)
States R is true (½ mark)

Revise the chapter

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

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 paper2026 board paper, set 430/1/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2026: question 20

Hints

Step-by-step solution

Revise the chapter

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