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.

MathsCBSE Class 10 · Standard · Board exam 2026, set 30/5/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Standard 2026: question 19

Set in the CBSE Class 10 board exam of 2026, paper 30/5/1, section A, question 19, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q19 · 1 mark · Assertion-reasonCompetency-basedPair of Linear Equations in Two Variables

Assertion (A): The system of linear equations $3 x - 5 y + 7 = 0$ and $- 6 x + 10 y + 14 = 0$ 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.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/5/1.

Hints

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

Hint 1

Compare the ratios $a_{1} / a_{2}$ , $b_{1} / b_{2}$ , $c_{1} / c_{2}$ .

Hint 2

Which two cases lead to no unique solution?

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.

$\frac{a _{1}}{a _{2}} = \frac{3}{- 6} = - \frac{1}{2}$ , $\frac{b _{1}}{b _{2}} = \frac{- 5}{10} = - \frac{1}{2}$ , $\frac{c _{1}}{c _{2}} = \frac{7}{14} = \frac{1}{2}$ . Since $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} \neq = \frac{c _{1}}{c _{2}}$ , lines are parallel: no solution, so A is true.
R is false: no unique solution may also mean coincident lines (infinitely many solutions). Option (C).
1 mark

Answer: Option (C)

Where the marks are

Shows A true by ratio test and R false due to coincident case (1 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 30/5/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2026: question 19

Hints

Step-by-step solution

Revise the chapter

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