MathsCBSE Class 10 · Basic · Board exam 2026, set 430/4/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2026: question 35(b)

Set in the CBSE Class 10 board exam of 2026, paper 430/4/1, section D, question 35(b), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q35(b) · 5 marks · Long answerPair of Linear Equations in Two Variables

Solve the following equations graphically : $x + y = 7$ and $2 x -5 y = 7$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/4/1.

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 equation.

Hint 2

For $2 x - 5 y = 7$ , choose x-values that make $2 x - 7$ divisible by 5 so y is a whole number.

Hint 3

The solution is the point where the two lines cross; verify 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.

For $x + y = 7$ , i.e. $y = 7 - x$ : table of values $x = 0, 1, 7$ gives $y = 7, 6, 0$ ; points $(0, 7), (1, 6), (7, 0)$ . Plot them and join to draw the line.
2 marks
For $2 x - 5 y = 7$ , i.e. $y = \frac{2 x - 7}{5}$ : table of values $x = 1, 3.5, 6$ gives $y = - 1, 0, 1$ ; points $(1, - 1), (3.5, 0), (6, 1)$ . Plot them and join to draw the second line.
2 marks
The two lines intersect at $(6, 1)$ . Check: $6 + 1 = 7$ and $2 (6) - 5 (1) = 7$ . Hence the solution is $x = 6, y = 1$ .
1 mark

Answer: $x = 6$ , $y = 1$ (lines meet at (6, 1))

Where the marks are

Correct points and line for $x + y = 7$ (2 marks)
Correct points and line for $2 x - 5 y = 7$ (2 marks)
Reads intersection: $x = 6$ , $y = 1$ (1 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 paper2026 board paper, set 430/4/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2026: question 35(b)

Hints

Step-by-step solution

Revise the chapter

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