MathsCBSE Class 10 · Standard · Sample paper, session 2026-27 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard sample paper 2026-27: question 3

From the official CBSE sample question paper for 2026-27, section A, question 3, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q3 · 1 mark · MCQPair of Linear Equations in Two Variables

Tarun correctly solved a pair of linear equations in two variables and found their only point of intersection as $(5, - 1)$ . One of the lines was $x - y = 6$ . Which of the following could have been the other line?
I: $3 x - 3 y = 18$
II: $2 x - 3 y = 13$
III: $2 x - 3 y = 16$

(A)I only
(B)II only
(C)I and II
(D)II and III

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2026-27.

Hints

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

Hint 1

Check whether (5, −1) satisfies each equation.

Hint 2

A line that coincides with x − y = 6 gives infinitely many solutions.

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.

I: $3 x - 3 y = 18$ is just $3 (x - y) = 3 \times 6$ . It is the same line as $x - y = 6$ , so the pair would have infinitely many solutions, not only one. I is rejected.
II: at $(5, - 1)$ , $2 (5) - 3 (- 1) = 13$ , so the point lies on it. Also $\frac{1}{2} \neq = \frac{- 1}{- 3}$ , so the lines intersect at exactly one point. II works.
1 mark
III: $2 (5) - 3 (- 1) = 13 \neq = 16$ , so $(5, - 1)$ does not lie on it. III is rejected.
Only II is possible, which is option (B).

Answer: II only, option (B)

Where the marks are

Checks each line for passing through (5, −1) with a unique intersection and selects II only (1 mark)

Revise the chapter

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

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 paperSample paper 2026-27 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard sample paper 2026-27: question 3

Hints

Step-by-step solution

Revise the chapter

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