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Graphs of two linear equations… (Class 10 Maths 2024, Q18)

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MathsCBSE Class 10 · Standard · Board exam 2024, set 30/1/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2024: question 18

Set in the CBSE Class 10 board exam of 2024, paper 30/1/1, section A, question 18, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q18 · 1 mark · MCQCompetency-basedPair of Linear Equations in Two Variables

In the given figure, graphs of two linear equations are shown. The pair of these linear equations is:

  1. (A)consistent with unique solution.
  2. (B)consistent with infinitely many solutions.
  3. (C)inconsistent.
  4. (D)inconsistent but can be made consistent by extending these lines.

Figure in the paper: Coordinate axes X-X1 and Y-Y1 meeting at O. Two straight lines are drawn, both sloping upward to the right, and they appear to be non-intersecting within the drawn region, i.e. parallel lines. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/1/1.

Hints

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

Hint 1

Compare the steepness of the two lines.

Hint 2

Lines with different slopes always intersect somewhere, even if outside the drawn region.

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.

  1. In the figure the two lines have different slopes (one is steeper than the other), so they are not parallel. Lines extend endlessly, as the arrows show.

  2. Two non-parallel lines meet at exactly one point. So the pair is consistent with a unique solution, which is option (A).

    1 mark

Answer: Consistent with unique solution, option (A)

Where the marks are

  • Recognises the lines are intersecting (different slopes), so the pair is consistent with a unique solution, option (A) (1 mark)

Revise the chapter

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 paper2024 board paper, set 30/1/1 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.