MathsCBSE Class 10 · Basic · Board exam 2025, set 430/3/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2025: question 21

Set in the CBSE Class 10 board exam of 2025, paper 430/3/1, section B, question 21, for 2 marks. Try it first; the hints and our step-by-step solution are below.

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

Solve the following system of equations graphically: $2 x - 3 y = - 6$ and $x = 3$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/3/1.

Hints

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

Hint 1

Find two or three points on $2 x - 3 y = - 6$ by choosing easy values of $x$ , such as $0$ and $- 3$ .

Hint 2

$x = 3$ is a vertical line. Where does the first line cross it? Put $x = 3$ into the first equation to check your graph.

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.

Table of values for $2 x - 3 y = - 6$ , i.e. $y = \frac{2 x + 6}{3}$ :
$x$ $- 3$ $0$ $3$
$y$ $0$ $2$ $4$
The line $x = 3$ is vertical and passes through $(3, 0)$ , $(3, 2)$ , $(3, 4)$ .
Plot $(- 3, 0)$ , $(0, 2)$ , $(3, 4)$ and join them to get the line $2 x - 3 y = - 6$ . Draw the vertical line $x = 3$ through $(3, 0)$ , parallel to the y-axis. Both lines are drawn on the same axes and labelled.
1½ marks
The two lines meet at $(3, 4)$ . So the solution is $x = 3, y = 4$ .
½ mark

$x$	$- 3$	$0$	$3$
$y$	$0$	$2$	$4$

Answer: x = 3, y = 4, i.e. the point (3, 4)

Where the marks are

Correct table of values and correct graphs of both lines $2 x - 3 y = - 6$ and $x = 3$ (1½ marks)
Reads the intersection point as the solution $x = 3, y = 4$ (½ mark)

Revise the chapter

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

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 430/3/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2025: question 21

Hints

Step-by-step solution

Revise the chapter

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