MathsCBSE Class 10 · Standard · Board exam 2025, set 30/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2025: question 28

Set in the CBSE Class 10 board exam of 2025, paper 30/5/1, section C, question 28, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q28 · 3 marks · Short answerPair of Linear Equations in Two Variables

Solve the following system of equations graphically:

$2 x - y - 2 = 0$

$- 4 x + y + 4 = 0$

Also, find the absolute difference between the ordinates of the points where given lines cut y-axis.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/5/1.

Hints

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

Hint 1

Make a table of at least two or three points for each line by choosing values of x.

Hint 2

The solution is the point where the two lines meet.

Hint 3

Put x = 0 in each equation to find where it cuts the y-axis.

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 $2 x - y - 2 = 0$ , i.e. $y = 2 x - 2$ : plot the points $(0, - 2)$ , $(1, 0)$ , $(2, 2)$ and join them to get line 1.
1 mark
For $- 4 x + y + 4 = 0$ , i.e. $y = 4 x - 4$ : plot the points $(0, - 4)$ , $(1, 0)$ , $(2, 4)$ and join them to get line 2, on the same axes.
1 mark
The two lines intersect at $(1, 0)$ , so the solution is $x = 1$ , $y = 0$ .
½ mark
Line 1 cuts the y-axis at $(0, - 2)$ and line 2 at $(0, - 4)$ . Absolute difference of ordinates $= ∣ - 2 - (- 4) ∣ = 2$ .
½ mark

Answer: $x = 1$ , $y = 0$ ; absolute difference = 2

Where the marks are

Table of points and correct graph of both lines (2 marks)
Solution $x = 1$ , $y = 0$ read from the intersection (½ mark)
Absolute difference of y-intercepts = 2 (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 paper2025 board paper, set 30/5/1 (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.

CBSE Class 10 Mathematics Standard 2025: question 28

Hints

Step-by-step solution

Revise the chapter

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