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Using graphical method, find… (Class 10 Maths 2023, Q21b)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/1/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2023: question 21(b)

Set in the CBSE Class 10 board exam of 2023, paper 30/1/1, section B, question 21(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21(b) · 2 marks · Very short answerPair of Linear Equations in Two Variables

Using graphical method, find whether following system of linear equations is consistent or not: and

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/1/1.

Hints

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

Hint 1

is one of the axes.

Hint 2

A system is consistent if the lines have at least one common point.

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. Draw both lines on the same axes:

    • is the -axis itself.
    • is a horizontal line through , passing through points such as .
    1 mark

  2. The lines intersect at exactly one point, . A unique solution exists, so the system is consistent.

    1 mark

Answer: Consistent; unique solution x = 0, y = −7

Where the marks are

  • Correct graphs of and (1 mark)
  • Notes the intersection at and concludes the system is consistent (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 paper2023 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.