MathsCBSE Class 10 · Standard · Board exam 2026, set 30/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2026: question 30

Set in the CBSE Class 10 board exam of 2026, paper 30/5/1, section C, question 30, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q30 · 3 marks · Short answerPair of Linear Equations in Two Variables

Solve the system of linear equations: $x = 4$ and $3 x - 2 y = 6$ graphically.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 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 three points for $3 x - 2 y = 6$ .

Hint 2

$x = 4$ is a vertical line through (4, 0).

Hint 3

The solution is the point where the two lines cross.

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 $3 x - 2 y = 6$ , i.e. $y = \frac{3 x - 6}{2}$ , table of values:
x 0 2 4
y –3 0 3
Plot (0, –3), (2, 0), (4, 3) on graph paper and join them to get a straight line.
1½ marks
$x = 4$ is a straight line parallel to the y-axis, at a distance of 4 units to the right of it, passing through (4, 0), (4, 3), (4, 5). Draw this line.
½ mark
The two lines intersect at the point (4, 3). Hence the solution is $x = 4$ , $y = 3$ . (Check: $3 (4) - 2 (3) = 6$ ✓)
1 mark

x	0	2	4
y	–3	0	3

Answer: $x = 4$ , $y = 3$ (lines meet at (4, 3))

Where the marks are

Correct table and graph of $3 x - 2 y = 6$ (1½ marks)
Correct graph of $x = 4$ (½ mark)
Reads intersection: $x = 4$ (½ mark), $y = 3$ (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 paper2026 board paper, set 30/5/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2026: question 30

Hints

Step-by-step solution

Revise the chapter

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