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

CBSE Class 10 Mathematics Standard 2026: question 34(a)

Set in the CBSE Class 10 board exam of 2026, paper 30/3/1, section D, question 34(a), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q34(a) · 5 marks · Long answerPair of Linear Equations in Two Variables

Solve the following system of equations graphically : $x - 2 y = 3$ , $3 x - 8 y = 7$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/3/1.

Hints

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

Hint 1

For each equation, find at least two or three points with convenient coordinates.

Hint 2

Write each equation as y in terms of x. Choose x-values that make y an integer, e.g. x = 3, 5 for the first and x = 5, −3 for the second.

Hint 3

The solution is the point where the two lines cross; check it in both equations.

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.

Line 1: $x - 2 y = 3$ , so $y = \frac{x - 3}{2}$ .
x 3 5 1
y 0 1 −1
Plot $(3, 0)$ , $(5, 1)$ and $(1, - 1)$ on graph paper and join them to get the line $x - 2 y = 3$ .
2 marks
Line 2: $3 x - 8 y = 7$ , so $y = \frac{3 x - 7}{8}$ .
x 5 −3 1
y 1 −2 −0.5
Plot $(5, 1)$ , $(- 3, - 2)$ and $(1, - 0.5)$ and join them to get the line $3 x - 8 y = 7$ .
2 marks
The two lines intersect at the point $(5, 1)$ .
Check: $5 - 2 (1) = 3$ ✓ and $3 (5) - 8 (1) = 7$ ✓.
Hence the solution is $x = 5$ , $y = 1$ .
1 mark

x	3	5	1
y	0	1	−1

x	5	−3	1
y	1	−2	−0.5

Answer: x = 5, y = 1 (lines intersect at (5, 1))

Where the marks are

Correct table and graph of $x - 2 y = 3$ (2 marks)
Correct table and graph of $3 x - 8 y = 7$ (2 marks)
Reads off the solution $x = 5$ (½ mark) and $y = 1$ (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 30/3/1 (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 2026: question 34(a)

Hints

Step-by-step solution

Revise the chapter

More questions from Pair of Linear Equations in Two Variables